Otis is a TranssexualOtis is a transsexual cow who was turned into a steer, but they forgot to remove the udders.
Alternately, Otis is a BifauxnenAnd a lesbian, apparently.
More Alternately, Otis is Intersex
The farmer is a Mad ScientistOtis (and, in The Movie, his "father" Ben) are the results of the farmer's sick, twisted experiments, creating a female cow with a male cow's personality, behaviors, and identity. Additionally, Freddie the "ferret" is actually an abomination created by the farmer by fusing several different species' genetic codes together into an unholy combination that does not even remotely resemble a real ferret in appearance or personality, and is only called such to hide the fact that he's actually the result of a disturbing fusion. Freddie's parents were also created by the farmer as additional cover-up - if they appear to be a family, then it's not nearly as obvious that they were engineered into existence.
The TV show is an alternate reality from the MovieBen and Daisy never existed. Otis "raised" himself growing up, what is why he can't even spell his own name on the show; nor has he learned his lessons on responsibility. Bessie arrived with the calf Joey (instead of Daisy) at the farm during the movie's timeline and Abby got their later (which is why Bessie knew who Wild-Mike was while Abby didn't). Duke, while he still isn't respected as leader, doesn't have the same deep rooted jealously that was seen in the movie either.