They're probably just making it clear that they'll populate their database with information for anime as well as for western TV shows. There's a very smooth distribution system for fan-translated anime so many people watch a lot of anime before it has aired outside Japan, and would want a database that keeps track of such viewing.

Anime and TV shows are like series, but Anime is the style (Japanese most of the time) and Anime has Anime Movies and Anime TV Shows, Anime OVA, etc

but isnt that just a categorisation like Crime, Drama, Comedy? Anf if not: how are other (non japanese) animated movies/series (justice league etc) treated?

Anime has it's own categories like Angst Ecchi Battle Royale edit Bullet Time Calling Your Attacks Collateral Damage Gunfights and a lot more. There are multiple websites that only feature Anime, and zero websites with full content about all three TV, Anime, Movies