Yep, they're all Jim Henson. And they show up on each other's stuff--Kermit was occasionally a newscaster on Sesame Street, and Big Bird was in the original Muppet Movie from the 70s.

The Muppets were created by Jim Henson in yhe 1950s, and made various appearances in commercials for the next 15 years.

Independently, Jim Henson was hired as a contractor to build puppets for Sesame Street. During the 70s the Muppets began to make appearances on the show.

Then in the mid-70s Henson made his own show, for British television, featuring a large cast of Muppets. This rocketed them to fame and spawned a series of feature films and spinoff shows that continues today.