Basic Trope: Sapient humanoid race with animal attributes.
Straight:
As Bob and Alice walk the Earth, they find a hidden valley populated by Cat Folk and befriend them.
In a Furry Fandom work, the protagonists are Petting Zoo People, and live in a universe where there's nothing unusual about that.
Exaggerated: Everyone in the setting is Petting Zoo People. Anthropomorphized animals of several different species, including predator and prey species, mingle and treat each other like humans.
Zig Zagged: Bob is a cat-man created by an Evilutionary Biologist. Alice is a Serkis Folk ratlike alien native to another planet. Charlie is a Wolf Man. Bob and Charlie get along like cats and dogs, but neither of them treats Alice like cats and dogs treat rats. They are all good friends and meet Dave, a snake-man, but no, Dave is just a guy in a costume, and the idea of snake-people is ridiculous. Or is it?
Averted: All animals in this setting are animal-shaped and no more intelligent than real animals, and all aliens are Starfish Aliens.
Enforced: "You know what's really popular these days? Furries. Our next series should have some."
Lampshaded: "Aw, come on! You know you can't stay mad at me for long! I'm part kitten!"
Invoked: In-universe, Bob is a member of the Furry Fandom. He seeks out Alice, the mad scientist, who is willing to turn him into a Petting Zoo Person For Science!!
Exploited:
Alice wants animal-related superpowers, but she's Genre Savvy enough to know that Monstrosity Equals Weakness, so she has to take a form that is pleasing to the eyes in order to gain powers without significant drawbacks.
Deconstructed: Alice meets Bob, a six-foot-tall bipedal cat made by an Evilutionary BiologistFor Science!. However, Bob's back is always killing him because a cat's legs and back aren't meant to move like a human's. Bob can't integrate into human society because he is treated like a freak. He'd really like to wear shoes and pants to blend into human society a little better, but he can't find any that fit, so he gets arrested for indecent exposure. He has a very hard time quelling his pounce instinct when he sees small dogs or human children running around.
Reconstructed: Bob is a cat-person, but the biologist or alien who made him knows what he was doing so a humanlike posture doesn't make him uncomfortable even if it looks weird, and the form comes with tradeoffs that are worth having, such as Super Senses. He's an oddity, but he lives in a Fantasy Kitchen Sink so it's not all that bad.