The Muppets are a veritable cornucopia of different species. Some are obviously Muppet versions of humans, like Statler and Waldorf...
... although it appears there's a distinction to be made between even Muppet humans and actual humans, judging by the song Man or Muppet from The Muppets (2011).
Some Muppets are apparently meant to belong to other subsets of the animal kingdom, such as Kermit the Frog, Fozzie Bear and Miss Piggy, who were clearly identified as a frog, bear, and pig, respectively, in The Muppet Movie (1979) (credit to PlutoThePlanet for this one).
Some are clearly identified as monsters:
Some as fruit or vegetables:
And some as aliens, like Gonzo, whose extraterrestrial origins were revealed in Muppets from Space.
This scene from Sesame Street Presents: Follow That Bird makes a clear distinction between "people" and the various other creatures that live on Sesame Street, emphasising the sheer diversity of life to be found there.
MISS FINCH: Hello, Big. Perhaps the dodos weren't perfect for you, but I have managed to find you another lovely bird family.
MARIA: He doesn't need another family. He has one right here, and we all love him.
MISS FINCH: But he's a bird. He'd be happier with his own kind.
MARIA: Well, we're all happy here on Sesame Street... and we've got all kinds. We've got people... and cows. And we've got... we've got Bert and Ernie. And there's dogs... and birds. We've got monsters... and kids. And there's honkers... why, we've even got grouches!
MISS FINCH: So you have. And you're all happy?
BIG BIRD: Yes, definitely.
MISS FINCH: Well... you did go to look for him, so that must mean you care. He does seem to have lots of friends, not feathered, but... all right. Big, from now on, Sesame Street is your home.
BIG BIRD: Oh, boy! Oh, boy! Oh, boy! Thank you!
MISS FINCH: Well, I've done it again. Placed another stray bird in a good home. Case dismissed. Back to work.
As far as anatomy is concerned, Muppets are apparently intended to be living, biological creatures with muscles, skeletons, digestive systems, etc.