Technically the words "funny animal" could be used for real-life critters who perform amusing stunts, like the contenders in Dave Letterman's "Stupid Pet Tricks." But it's generally used as it is in this Wiki-page: to signify creatures who are anthropomorphic in some way.
One variety is the fully humanized animal, who regularly walks on two legs, may wear clothes like a human, and who frequently interacts with cartoon versions of human beings.
Another type behaves in some ways like an amimal, and usually walks (or flies, or swims) as its real-world counterpart does. However, at any time such types can "take a break" and do identifiably human things.
They may do nothing more than think coherent thoughts, like the titular star of Disney's 1964 film THE THREE LIVES OF THOMASINA.
They may imitate only a few human actions, like standing on two legs. as Garfield often does. A
related but more outrageous type like Snoopy doesn't regularly wear clothes but can don them whenever he wants to take on another identity.
Some continue to go on all fours but can talk like-- and even to-- human beings, a la Scooby-Doo.
It's clear that in a purely technical sense, all of these types fall into the phenomenal category I call "the marvelous." And yet it's clear from my studies of other compendia of metaphenomenal films that often this species of marvelous phenomenon is given a "pass." To my knowledge no such compendium has ever included 1972's SNOOPY, COME HOME, in spite of its walking, coherent-thinking "funny animal." Similarly, in the essay ON FAIRY STORIES, Tolkien's great examination of the nature of fantasy, he excluded animal fables like those of Aesop from his realm of faerie.
I can well understand Tolkien's reticence. Features in which the characters look like humanized animals but essentially act like human beings generally fail to transmit what Tolkien called the "arresting strangeness" of fantasy. Mickey Mouse animated cartoons may at least have the mouse doing impossible things, but the Floyd Gottfredson comic strip was more like a rural comedy-adventure that just happened to star humanized mice, horses, etc. The erotic anthropomorphic comic book OMAHA CAT DANCER only rarely referenced the animal natures of the characters, whose adventures usually fell into the realm of soap-operatic melodrama.
It's as if funny animals have a certain "invisibility" in certain contexts: they're so obviously stand-ins for human beings that one doesn't think of them as "marvels" at all. I'm tempted to regard some of them, like the casts of OMAHA and the MICKEY MOUSE comic strip as belonging to the naturalistic version of my narrative trope "delirious dreams and fallacious fantasies." However, to qualify as a "fallacious fantasy," the fantasy would have to be a phenomenon that was simply a departure from the work's diegetic "reality" that the audience was not expected to take seriously. An example of this would be the animated "Pink Panther" from the live-action PINK PANTHER films, who may comments upon, but is not involved in, the "reality" of those movie narratives.
In conclusion, I can only note that although many funny-animal works technically belong to the category of the marvelous, they often evoke so little of the affects of wonder and strangeness that they almost constitute an "attack" on their own domain.