Stop-frame or single-frame animation goes at least as far back as King Kong in 1933. The animator was Willis O’Brien, who used puppets supported inside by metal armatures that could be rigidly positioned and posed. He inspired Ray Harryhausen, legendary stop-frame animator of the 1950s & 60s.
Clay animation is a different technique with a different “look and feel.” Both require highly talented artists to pull off the illusion of natural motion so well. As a youngster I dabbled with Super-8 single-frame animation—makes you appreciate the work involved.
Here’s a video of the making of Fantastic Mr. Fox. It’s basically the same process. (The fur & clothing were especially well done.) They shot over 600,000 individual frames.