Correct. But the genre names usually have a history how they originated. Problem is, while the games changes, the names of genres did not. It's a mess. To be honest, it was a mess from the beginning, but it got worse over time.

I personally see "genres" like tags grouping a game in a few words. With the possibilities and variety of games of today and the ancient genre names of the past, classifying games based on a single genre name does not workout always, especially with terms as broad as Action/Adventure. We even have genres or "game types" named after games titles, such as "Metroidvania", "Souls-like" or even "Breath-like" (yeah, some use that term too...).

Some even classify GTA as a racing game; it's ridiculous! But on the other hand, sometimes genres are descriptive of what the game is about to a certain degree "Fighting", "Racing" or "MOBA" are examples of useful groups. That does not mean games can't be classified in multiple groups (hence why I said it makes most sense to use these like tags).