In adjective form, they are. Fur and hair are two different things, though. While they serve the same basic purposes, they are different in themselves. Particularly in their growth. Fur is typically fuller, but grows to a set length, whereas hair just continuously grows. Fur also typically sheds while hair remains. Some scientists and doctors recognize them as synonyms, as they basically are the same thing, but there is a bit of a difference when it comes down to it. :o
Hair is fur and fur is hair. Fur isn't fuller, there's just more of it. It doesn't grow to a set length, it sheds fast enough so that it seems like it. Hair however, also sheds but much much slower, so that hair will seem to grow over time. They are the same but the rate at which they shed are different.