Vocab lesson time: animation isn't a genre. It's a medium or technique. Toy Story might be a cartoon that's made on a computer, but that doesn't mean it's not on par with live-action movies with real people's faces filling up frame.
(Actually, it's way, way better than a lot of those.)
In fact, like many live-action movies before it, Toy Story is also a buddy comedy. Basically, a buddy comedy is all about two guys who hang out and do friend stuff (mostly with hilarious results).
Of course, this buddy comedy involves two characters—Woody and Buzz—who don't like each other much. Think of it in the same vein as The Odd Couple or Lethal Weapon—two guys who seem to be complete opposites bond and grow to become friends through adversity. Gee, we guess we're glad that Sid kidnapped and tortured them after all.
And, since Toy Story was made with kids of all ages in mind, we're going to go ahead and classify it as family entertainment, too. Sure, because this is a cartoon we're talking about, you might think that this film is for the little tikes only, but Toy Story has tons of themes, characters, and jokes that will appeal to the grown-ups in the room. (Remember when Bo Peep offers to find someone else to watch the sheep tonight? Bow chicka bow bow.)
This one is fun for the whole family—and when we say that we actually mean it. Grandmas will like it as much as kindergarteners or college kids…because it's Grade A quality Pixar goodness.