Hmm... not exactly. There isn't a great deal of Animal Crossing stuff here. I don't really remember the Chao stuff from Sonic really, either. I didn't fiddle much with that game for some reason, despite liking it.
Anyway, it basically boils down to you meeting various requirements to first attract an animal (say you have to have so much grass or water or kind of fruit or other animal), then once it visits, you have to meet certain requirements to get it to stay (usually giving it things to eat and such). After that, you have to get it to breed by building it a house and meeting other requirements, and then you generally use that animal population as a kind of stepping stone to achieve other goals. It really builds on itself. And this sounds horribly tedious, I know, but it doesn't play that way at all because you generally aren't rushed into doing anything, there's a constant feeling of progression because you earn experience and unlock new things, and there are some various little side challenges and things that pop up. Plus just building the garden can be very fun and rewarding, especially if you make it look cool, and you can go a million different routes trying to move up the food chain to more desirable animals.