@gay_ornithischians @korewaChino @AmyIsCoolz @puniko @amelie @ek_is_anika @alice @lea @lurid_ginger
It's fairly simple really:

Furries are full animals who move, talk and walk like humans, developed by western cartoon "funny animal" fandom.

Catgirls are humans with cat ears, tail and personality mannerisms, evolved from Japanese folklore where girls who act consistently naughty may turn into cats. Therefor, catgirls were (and still are) used in manga/anime to visualize a 'naughty person' who's up to no good.

So, different background, different genus, different cultural origins. Very separate things.