These are both mustelids, or in the weasel family. the group Mustelids/weasels are to these guys what the group Canines are to dogs and foxes and wolves and things.
But within that group, these guys aren't actually very closely related. Each of these "badgers" is roughly as equally related to each other as they are to these other mustelids
bonus pic because i'm not sure people understand wolverine size
Anyway, both types of badger are fascinating, but they are very different.
The American Badger is volatile and ferocious. They are largely solitary, and don't dig their own burrows so much as murder a burrowing creature, eat them, and then remodel that burrow for themselves.
European Badgers live in communal dens, and dig activity-specific rooms, including a separate toilet room. They will sometimes have a networked multi-family den/burrow system, with a large extended family all having their own underground homes that are attached to each other. European Badgers will sometimes share their borrow amicably with foxes, rabbits, or raccoon dogs (which exist in the wilds of europe after having been introduced).
The denning with rabbits is interesting since rabbits are often a prey item for European Badgers, whereas the foxes and raccoon dogs are weird roommates for them because they have heavily overlapping diets and are direct competition for one another.
While they do often eat birds and small mammals, European Badgers will happily exist on a diet of earthworms, insects, fungus, and various plants... and so will red foxes. They are both extreme generalists, eating basically anything available.
American Badgers on the other hand... while they will eat worms and fungus and fruit in small amounts or if very hungry, they primarily eat small mammals, about 10 species of rodent, with some birds and insects and reptiles thrown in along with whatever larger animals they can scavenge. American badgers have been known to bury an entire deer or even cow carcass to eat later. They are bloodthirsty and voracious.
So... OP's take is not wrong. European Badgers will build and share little den villages and they eat a lot more worms and fruits and grains...
while American Badgers steal temporary homes by murdering and devouring the previous occupants, and would generally prefer to eat as large an animal as they can get.
But don't let that fool you. Look back through those pictures. The European Badger is still in the family, and their butler persona is a lot like Alfred's the way they will get out the big guns for an enemy with zero hesitation and no fucks given.
BONUS bonus pic, here is my dog, who is about the same size as a badger, who has a stripey nose like a badger, and who's name is, in fact, Badger
