Species vs. Behavior (I couldn't find anything for the blank ones)

Dog-like dog = Santa's Little Helper - The Simpsons

Person-like dog = Jake - Adventure Time

Cat-like cat = Cat - Stray

Person-like cat = Meowth - Pokémon (specifically the anime)

Dog-like person = Spot - The Good Dinosaur

Cat-like person = Garfield - MeatCanyon

Person-like person = "Weird Al" Yankovic

Dog-like thing = Chain Chomp - Mario

Cat-like thing = Gary - SpongeBob SquarePants

Person-like thing = Jenny - My Life as a Teenage Robot