On the one hand, it's true that the way Dungeons & Dragons defines terms like "sorcerer" and "warlock" and "wizard" is really only relevant to Dungeons & Dragons and its associated media – indeed, how these terms are used isn't even consistent between editions of D&D! – and trying to apply them in other contexts is rarely productive.
On the other hand, it's not true that these sorts of fine-grained taxonomies of types of magic are strictly a D&D-ism and never occur elsewhere. That folks make this argument is typically a symptom of being unfamiliar with Dungeons & Dragons' source material. D&D's main inspirations are American literary sword and sorcery fantasy spanning roughly the 1930s through the early 1980s, and fine-grained taxonomies of magic users absolutely do appear in these sources; they just aren't anything like as consistent as the folks who try to cram everything into the sorcerer/warlock/wizard model would prefer.
For example, in Lyndon Hardy's "Five Magics" series, the five types of magical practitioners are:
Alchemists: Drawing forth the hidden virtues of common materials to craft magic potions; limited by the fact that the outcomes of their formulas are partially random.
Magicians: Crafting enchanted items through complex manufacturing procedures; limited by the fact that each step in the procedure must be performed perfectly with no margin for error.
Sorcerers: Speaking verbal formulas to basically hack other people's minds, permitting illusion-craft and mind control; limited by the fact that the exercise of their art eventually kills them.
Thaumaturges: Shaping matter by manipulating miniature models; limited by the need to draw on outside sources like fires or flywheels to make up the resulting kinetic energy deficit.
Wizards: Summoning and binding demons from other dimensions; limited by the fact that the binding ritual exposes them to mental domination by the summoned demon if their will is weak.
"Warlock", meanwhile, isn't a type of practitioner, but does appear as pejorative term for a wizard who's lost a contest of wills with one of their own summoned demons.
Conversely, Lawrence Watt-Evans' "Legends of Ethshar" series includes such types of magic-users as:
Sorcerers: Channelling power through metal talismans to produce fixed effects; in the time of the novels, talisman-craft is largely a lost art, and most sorcerers use found or inherited talismans.
Theurges: Summoning gods; the setting's gods have no interest in human worship, but are bound not to interfere in the mortal world unless summoned, and are thus amenable to cutting deals.
Warlocks: Wielding X-Men style psychokinesis by virtue of their attunement to the telepathic whispers emanating from the wreckage of a crashed alien starship. (They're the edgy ones!)
Witches: Producing improvisational effects mostly related to healing, telepathy, precognition, and minor telekinesis by drawing on their own internal energy.
Wizards: Drawing down the infinite power of Chaos and shaping it with complex rituals. Basically D&D wizards, albeit with a much greater propensity for exploding.
You'll note that both taxonomies include something called a "sorcerer", something called a "warlock", and something called a "wizard", but what those terms mean in their respective contexts agrees neither with the Dungeons & Dragons definitions, nor with each other.
(Admittedly, these examples are from the 1980s, and are thus not free of D&D's influence; I picked them because they both happened to use all three of the terms in question in ways that are at odds with how D&D uses them. You can find similar taxonomies of magic use in earlier works, but I would have had to use many more examples to offer multiple competing definitions of each of "sorcerer", "warlock" and "wizard", and this post is already long enough!)
So basically what I'm saying is giving people a hard time about using these terms "wrong" – particularly if your objection is that they're not using them in a way that's congruent with however D&D's flavour of the week uses them – makes you a dick, but simply having this sort of taxonomy has a rich history within the genre. Wizard phylogeny is a time-honoured tradition!
