When Clifford first appeared on The Jim Henson Hour, he was the bassist for a group called "Solid Foam." He had a slightly different look, and always wore sunglasses. But I remember thinking when I first saw him, "cool...the Muppet guys made a Bob Marley-ish character."
The next time I saw him was on Muppets Tonight (although he apparently made guest appearances on other shows in the early 90s). The MT version was a remodeled version of the original, and didn't wear sunglasses. But I always accepted the fact he was human or humanoid.