For starters, I'm not an expert on such things, so what I may say may not mean a whole hill of beans around these parts.
A "Muppet" is a combination of traits that originally made up marionettes and puppets. Muppets have features prominent in both of those storytelling devices. The term was created by Jim Henson to describe his particular creations. They weren't exactly marionettes and they weren't exactly puppets in the traditional sense, so Mr. Henson created the term "muppet" to describe his creations.
The legality of the term "muppet" is kind of strange, especially since Muppets have been used to describe any creation from Jim Henson Productions. Every performance made by the Henson troupe of "muppeteers" from Ed Sullivan to Sesame Street to Saturday Night Live had the name Jim Henson's Muppets attached to them. However, with The Muppet Show, the term "Muppet" became prominent with the particular circle of characters, even though JHP continued performing characters on Sesame Street. It's just around this time that the term "Muppets" became universally accepted for every production made by the Henson troupe of performers.
Various films and productions proceeded to connect the worlds created by JHP. Characters introduced on shows like Fraggle Rock, and Bear in the Big Blue House, Mother Goose Stories, Animal Show, Animal Jam, and The Storyteller as well as specials like Emmitt Otter's Jug Band and Dog City were "muppets" in the technical sense but not "Muppets" in the marketable brandwise sense.
While the franchises of the original Jim Henson Productions was divided (all the Sesame Street [and I think Big Bag] characters are owned by Sesame Workshop, the Bear in the Big Blue House franchise and the core Muppetverse characters are owned by Disney, while Farscape, Fraggle Rock, and the remaining franchises are owned by JHP), the term "Muppet" could be universally used for those characters. I haven't looked at Sesame Street since they turned half of it into *blech* Elmo's World, so could anybody clue me in as to whether they still refer to the Sesame Street Muppet characters as Sesame Street Muppets? I believe Disney bought the term "Muppet" when they bought the Muppetverse characters, but under certain circumstances, they'll allow JHP and SW to continue using the term to refer to those characters since they're so synonymous with the Jim Henson name and Sesame Streeet brand.
If Disney won't, then they're a strange bunch of gits, aren't they?
Don't know if this answered the question, but it's my four half-cents on the topic.