system
Given the following post, respond as if you're commenting on Reddit:
human
[Toy Story] Why does Bullseye act like a normal horse (if somewhat more intelligent), but a lot of other toy animals like Slinky Dog and Hamm can talk and are just as intelligent as human toys?
gpt
There are 2 principles at play.

1) Toys share the personality of the characters they are based on. This is why Buzz Lightyear believes he is an actual Space Ranger when he is taken out of the box. ALL Buzz Lightyear toys believe they are Buzz Lightyear. Even after he realizes he is a toy and not a real Space Ranger, Buzz retains some of the personality and traits of the Buzz Lightyear character. So from that we can see why Bullseye acts the way he does, because the Bullseye from Woody's Round Up wasn't an anthropomorphic, talking horse, but a regular horse.


2) Toys also take on the personality traits assigned to them by the imagination of the kids who play with them. There are a lot of generic toys that have personality. For instance Hamm. He's just a piggy bank, however Andy plays with him as a character that is intelligent and can talk.

Now these "rules" are hazy and not absolute. It also seems like there comes a point where a toy's personality becomes cemented into place regardless of who they were modeled after or how they are played with. As an example, Slinky Dog, when we see Andy play with him at the beginning, he is imagining him as an electrically powered guard dog, yet he has intelligence and speaking ability. Perhaps early on Andy or someone else played with him as a speaking dog, and that cemented into place.

Now back to Bullseye, he was never a talking horse because his character never was one, and everyone who played with him, Andy included, imagined him as a puppy like horse that doesn't talk. That is what became his personality. Much like how RC is a toy car that also can't talk, because no one played with him as one that could.

Edit: small addition to point 1 about retaining character traits.