As others have explained, the Muppet characters are all pretty much what they seem to be. Kermit is a frog, Miss Piggy is a pig, Cookie Monster and Elmo are monsters, etc. The history of many of them have been shown in the Muppets and Sesame Street universe, and they're consistent with the types of beings that they identify as.
But like many animals in fiction, they're anthropomorphized. They can speak, drive, ride bicycles, own property, etc.
One of the things that Sesame Street tries to teach children is ideas of inclusion and tolerance. The human cast has been diverse since the start, and having the humans and non-humans treat each other as equals drives home this concept. There's no discrimination in the Sesame Street universe.
This is less so in the more adult Muppet Show universe, but the characters who discriminate against the Muppets are always the villains. This is a clear metaphor for the evils of racism.