i love JayTim so dearly and i do ship them, but a lot of the propaganda is incorrect (and by extension is very common misinformation in the fandom) so i'd like to clarify. (note: this is not meant to be hate toward the OP! i know the propaganda was not written by the person running the blog, and whoever did write the propaganda also doesn't deserve hate! it's okay to be wrong in fandom! warning: this post is long.)
for our intents and purposes, the canon(s) featuring these two fall into three main categories: pre-Flashpoint (aka: Post-Crisis or preboot), New-52, and Rebirth. for simplicity's sake, i will not be taking adaptations such as Titans (tv) or Gotham Knights (game) into account, as they aren't the primary source people use for ship fodder. breaking this down bit by bit i want to start with:
Jason and Tim are under two years apart in the pre-Flashpoint canon. they meet when Tim is 16 and Jason is 18. when pre-Flashpoint ends, they are 17 and 19 respectively. it's also noteworthy that Jason was dead for six months in-universe, and did not age physically or mentally in this time frame. they meet as teenagers and consider each other in the same peer group. in fact, it's Tim who seems to view Jason as a child/immature (referring to him as such during the Search For A Hero arc of Robin [1993]) meanwhile Jason only seems to view Tim as his peer and even extends respect to him in this way. less than two years doesn't qualify as an age gap imo, especially given they met when they were both older teenagers.
in the New-52 canon, the ages are much more contradictory. constructing a timeline with comics is difficult, but the New-52 *especially* regularly contradicts itself on the timeline. that said, Tim is likely 16 at his introduction in this continuity, and Jason is 18, possibly 19. which once again, gives them a gap of about two years. at best, you could argue Jason is around 20, but that seems unlikely, given how quickly he is introduced after his return as Red Hood. once again, it's worth noting in this continuity he was dead for about six months and did not age.
the Rebirth canon is an extension of the New-52 timeline and thus, *should* keep the New-52 age gap of about two years. however, it does seem like Rebirth has been pushing Jason closer to Dick Grayson's age group (Dick should be about six years older than Jason and eight years older than Tim) with no real explanation, as we've seen Jason more heavily interacting with characters in Dick's age range (Roy Harper, Starfire, etc). this seems to age Jason, to put him on par with those characters. it doesn't help that DC hasn't aged Tim on page, and logically Tim should be in his 20s by now as Dick is nearing his 30s (Dick and Tim's age gap is crucial for Tim's backstory to work but that's a different issue entirely) which would keep Tim and Jason mostly consistent. however, since we haven't seen on-page confirmation of Tim's age, this is where i believe fans falsely assume there's an age gap. most people assume that Jason is currently in his mid-20s and Tim is still 17. given that we have seen every other character age around Tim and haven't had any comic indicate Tim *hasn't* aged, the safest assumption is that he has, and is likely around 21, with Jason around 23. they should be (and by any logical assumption, are) in their early 20s together. this is also likely bc in Tim Drake: Robin, Tim lives on his own on a boat he bought, and his boyfriend (who is the same age as him) is in college. them being further apart is entirely fanon, or misconstrued canon.
this is a far more subjective one that's difficult to quantify based on what you personally consider to be an abusive relationship. but in this case, i think it's wildly incorrect. the better term here would be antagonistic.
in the pre-Flashpoint canon, Jason and Tim are almost always on opposite sides and fight during most of their interactions. however, these are mutual fights due to conflicting morals and goals, given Tim is a vigilante hero and Jason tends to be a villain during this era. the main fights these two get into are:
Teen Titans (2003) #29 - the well-known Titans Tower Incident, where Jason ambushes and attacks Tim at Titans Tower. this is the most unbalanced of all their fights and the only one i would almost consider "abusive", but it was an equal fight. Jason beats Tim, but the common fandom misconception that Tim was afraid of Jason and seriously injured by this event is untrue. Tim was insulting Jason the entire time and seemed to come out of the fight with only a few bruises. they fought because of their disagreements on Batman and teenage vigilantes, not because of personal issues. (they did not know each other prior to this, aside from a brief meeting during Batman: Hush, in which Jason did cut Tim's throat, but once again, this was to antagonize Batman)
Robin: Search For A Hero - this fight was over a budding gang war in Gotham, in which Jason and Tim had vastly different beliefs on how it should be handled. it's worth noting in this fight, Jason actually approaches Tim to ask Tim to work with him. the fight is mutually instigated when Tim says no, and Tim ultimately wins when Jason is arrested. the root of this fight was conflicting morals, not personal issues with each other. neither sought the other out to abuse them.
Battle For The Cowl - this fight was once again, instigated mutually (though mostly by Tim, who hunted Jason down) over conflicting morals, as Jason at this point had begun mass murdering people in a Batman suit. Tim confronts him (also in a Batman suit) and they have their most bloody fight, the only fight where Jason arguably was actually trying to kill Tim. they are the most cruel to each other and there is a clear personal hatred, but this comic is notoriously out of character, especially for Jason. still, the conflict was moral, not personal, and certainly not abusive.
aside from these instances, Jason and Tim do not routinely seek the other out to cause physical or mental harm. there is no habitual cruelty they enact upon each other, they are just enemies in the hero/villain sense.
in the New-52 canon, Jason and Tim actually get along quite well. we are introduced to them being very close, and thinking of each other fondly. they work together and are not antagonistic, as Jason is at worst, an antihero during this era and at best, just another vigilante in the Batfamily who's slightly more violent. Jason and Tim have two significant fights, both of which are forced by external forces. in Robin War, the Court of Owls forces them to fight to the death and in Death of the Family, the Joker forces them to fight to the death. both times, they are able to plan a way out of the fight without needed to speak to each other and make it clear they only fought for show.
in Rebirth, the closeness of Jason and Tim isn't as highlighted upon as it is in New-52, but it's still entirely civil and they seem to care for each other. they easily work together in comics such as Robin: Knight Terrors, and once again seem to always be on the same side. when Jason and Tim are on the same side in a fight, they always easily get along.
the Underage and Psuedo-Incest do both qualify here since Tim was technically underage during their first meeting in both continuities and there's the ever-present "technically Bruce Wayne adopted both of them." (though it's worth noting there is no canon where Tim and Jason view each other as brothers. the closest they come is the New-52, where even then they mock the idea of being brothers. they are familial at best, but given they've never had time to significantly develop a domestic bond, it's reductive to consider them to be just brothers because the same guy signed their adoption papers.)
""We're both outsiders in a family of outsiders." - Jason Todd about Himself and Tim Drake
this is true, but only as a part of the New-52 canon. Jason specifically says this during the Robin War arc, though this theme of "outsiders of the outsides" continues throughout the New-52 during all of their significant team-ups and is used to depict the unique bond they have within the larger Batfamily.
Baby Tim did canonly stalk Jason when he was Robin. Jason definitely stalked Tim and had a photo wall for Tim.
this is wildly untrue on both accounts. as for Tim, the only time we see "stalkerish" behavior exhibited is during A Lonely Place of Dying, which is Tim's introduction in the main Batman run, in the pre-Flashpoint timeline. we do see panels of him with a camera to take pictures of Batman and Robin, but nothing implies this was a consistent habit, just a one-time thing to prove his theory about the identities of Batman and Robin. we never see him depicted with a camera in this context again, nor have we any proof this was a regular thing he did as a child. furthermore, the Robin he took pictures of was Dick Grayson. Dick was Tim's childhood hero (because he met Dick when Dick was a Flying Grayson), not Jason. we have nothing to indicate Tim was stalking Batman and Robin during Jason's tenure.
moreover, from the information we do have about Tim's feelings on Jason while Jason was dead, Tim doesn't hold Jason to a heroic idol status. this is very common fanon/misinformation, the idea of stalker!Tim in general, but especially in relation to Tim stalking Jason specifically. (and once again, calling Tim a "baby" seems like an exaggeration, as Jason would've been 14/15 and Tim 12/13 during this time frame, if this happened). during Detective Comics: Rite of Passage, the arc that leads to Tim becoming Robin, Tim does respect Jason's legacy and holds it to a high standard. but these feelings do not revolve Jason as a person and instead, the idea of the second Robin who died in the mantle, and how that legacy proves the danger Tim faces when he takes on the mantle.
later on in Batman (1940) #456 when Tim is Robin, we do see Tim hallucinate/daydream Jason cheering him on, though Tim also internally views Jason's death as Jason's fault, due to his own impulsiveness and inability to follow orders. Tim's opinion of Jason during this time was neutral, leaning on victim blaming. there was no hero worship or stalking.
on Jason's side of things, once again, there is no stalking behavior. it is true Jason briefly had a photo wall of Tim! this is again the pre-Flashpoint timeline (in the New-52/Rebirth, we only ever see Jason and Tim as an established friendship, we don't have much information on how or when they met, or their feelings on each other prior to meeting) specifically in Red Hood: Lost Days. however, Jason did not take these pictures. Talia al Ghul gave him the pictures to show him that Batman had replaced him with a new Robin. Jason was the one who put the pictures on his wall, just to angst and be weird over them, which certainly makes him unwell about Tim, but it was never stalking behavior.
Jason says that Tim is the only BatFam member who doesn't make him want to throw up. At one point he asks Tim to be his Robin and when Tim says no he immediately beats the shit out of him and shoots him."
the first account is true, Jason does say this about Tim. once again, in Robin War, during the New-52 timeline. i think this was a slight exaggeration on Jason's part, as he tended to speak in hyperbole during that run, but at the very least he was truthful about the general sentiment of preferring Tim above everyone else in the Batfamily.
the second account is true but more complicated. firstly, this is the pre-Flashpoint timeline, so to mash it together with things Jason has said about Tim in the New-52 is shoving two different canons together, where Tim and Jason held wildly different relationships. secondly, Jason says this during their fight in Battle For The Cowl. which as said above, was wildly out of character for Jason. it's noteworthy that Jason also asks Dick to be his Robin just one issue later, so this offer wasn't entirely unique to Tim. Jason does respect Tim and thinks Tim has a lot of great potential that's being held back by his loyalty to Bruce (the only part of BftC that is in character for Jason, tbh).
however, to be slightly pedantic, Jason does not shoot Tim during this encounter. when Tim says no, Jason stabs him in the chest with a batarang and leaves him for dead, then claims he killed Tim later on.
these two are unwell about each other in every canon, and even at their most antagonistic have some wild complexes about each other. this poll left out some of their other fun moments, such as during the pre-Flashpoint timeline, Tim broke Jason out of prison for no real reason (Search For A Hero). or during the New-52, Tim is able to recognize Jason by his smell alone (Death of the Family). they are always incapable of being normal about each other and their antagonistic history does make it such a fun ship, even when you strip away the parts that are misinformation. and to be fair, the fanon misinfo is still fun for headcanons and fanfic! it's just that this fandom often confuses canon and fanon.