muppet-facts:
Hi! I totally get the argument, as it is one I’ve had with others a lot lol
So, all Muppets are puppets, but not all puppets are Muppets is a way I like to start thinking about it. Like you said “Muppet” is a portmanteau of marionette and puppet, but the origin of the word is often refuted. Henson said on some occasions that this origin is true, and on others, he just said he liked the sound of the word. There’s lots of evidence for both sides, but I think it’s important to note that “Muppet” doesn’t just mean a creature using the combination of those two methods of puppetry. Otherwise, full-bodied Muppets, like Sweetums and Big Bird, wouldn’t be considered “Muppets.”
But anyway back to the real question: Are all Jim Henson creatures Muppets? I do understand the desire to only put puppets of the cartoonish aesthetic into the category of “Muppet,” as it seems most cohesive, like Fraggles and the Muppet troupe. But does that make only Sir Didymus and Ambrosius the only puppets in Labyrinth to be “Muppets?” Does that mean Kira and Jen are not “Muppets” but rather Jim Henson puppets?
Some Jim Henson productions have said things like “featuring Jim Henson’s Muppets” somewhere in the product, like the subtitle or credits, the implication being the puppets that appear are “Muppets.” This would make Fraggles “Muppets,” since the show is also known as Fraggle Rock with Jim Henson’s Muppets. To your question about Sesame Street, some books like The Sesame Street Treasury, have a subtitle that says “featuring Jim Henson’s Sesame Street Muppets,” which would go to show these characters are “Muppets.”
Without this whole list of technicalities, I’d say, sure, all Jim Henson puppets are “Muppets,” and even with these technicalities, I’d still say yes - all Jim Henson puppets are Muppets. There is a “traditional” idea of what a “Muppet” is, but the concept has evolved from simply referring to puppets with Rowlf’s aesthetic. I think it’s more fun to think of this wild and fun menagerie of puppets as all being Muppets.