Here let me copy paste from someone that explains it better than me LOL ''Anthropormorphic simply means ANYTHING that is not human morphed into human form (or possessing a human personality.) It could be a chair, an animal, a banana, an M&M. Literally anything.
"Furry" just refers to animals being anthro. However, the animal does not have to have fur. Its just a term. Snakes lizards, and dragons ect can also belong in the furry fandom because they are still anthro animals.
So they basically mean the same thing, but you'd use them in different contexts''