What's the difference between a muppet and a puppet?
Absolutely nothing. This is like asking "what’s the difference between a poodle and a dog?" Think about it - a poodle is a dog, but not all dogs are poodles. So a muppet is simple to figure out: it’s a type of puppet (usually placed under the category of ‘mouth puppets‘). Not all puppets are muppets though, and not all mouth puppets are muppets.
But there is something tricky about the term ‘muppet’. Technically, the only people who can use that name is The Muppets Studio (a part of the Walt Disney Company) as it’s a registered trademark. Henson invented the term to refer to his foam puppets, combining the word "marionette" with the word "puppet". So if we’re talking about any muppet made by the Studio, we’re talking about it in the official capacity: in this case, a muppet is a certain type of puppet made only by the Studio, and is different to all other puppets for that reason.
But here on this site, and elsewhere, you’ll find people talking about muppet-type puppets or muppet-style puppets… even rod arm puppets or glove arm puppets (the first uses rods for operating the hands, the second uses gloves and human hands in place of the puppet’s hands). What’s the difference? Nothing. It’s the same methodology of puppet building, similar character styles, similar materials. It’s just we prefer not to get sued for infringement of copyright, so we use a different term when referring to our muppet puppets. In this case, any muppet not made by the Muppets Studio is a muppet-type puppet, and we’re talking about them in an unofficial capacity; a muppet-type puppet is a certain type of puppet made by anyone, and is simply a term used to refer to a particular building method or design of a mouth puppet.
Does that make sense? Again, the simplest way to remember it is with the dog analogy. A muppet or a muppet-type puppet is a type of puppet, just as a poodle is a type of dog.
Additionally, there is no such thing as a ‘muppet finger’ puppet or a ‘muppet shadow’ puppet, etc. It’s most likely that those who are using those terms are confusing the word ‘muppet’ with the word ‘puppet’, because they don’t know much about puppets and have only been exposed to Henson’s work.
UPDATE: After thinking about it, I thought I would also add a few words about Henson’s Creatures. Jim Henson and his company often made - and still do - ‘creatures’. These are separate designs from muppets, and are animatronic puppets. Most familiar to people are Henson’s Creatures presented in films like The Dark Crystal and Labyrinth. So it should also be clear to members of the public that not all Henson puppets are muppets either; in fact, these days the Henson company also do digital animation too!
Learn how to make a muppet-type puppet here and here!
This post AKA what type of puppets are used in the muppets

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