I should note, although it’s not directly relevant to your point, that “people who eat vegetables (instead of meat)” are also called vegetarian. The precise degree to which oppression of animals is tolerable was a contencious debate among vegetarians, which led to the creation of “The Vegan Society” to rally those that argued for “no oppression at all”. So even though dairy and egg farming require animal murder (to deal with the newborns considered a “byproduct”) vegetarians don’t object to those.

Vegans however take the idea that animals are thinking, feeling creatures to its logical conclusion and will argue for no animal products anywhere. No leather, no beeswax, no brushes with animal hair, no trips to the zoo, no pets and so on. It’s very much not just the diet, although that is of course a huge part of it.