People talk about how Michael Caine treated the Muppets like actors and how Tim Curry treated himself like one of the Muppets, but I haven't seen people talk about of the films approach the source material in the same way.
The Muppets' Christmas Carol researched 1800s clothes to make the costumes accurate for both Muppet & Human actors & had Gonzo quoting Dickens's prose straight up. There were some jokes in there but for the most part the story maintained an atmosphere that you'd expect from a traditional Christmas Carol adaptation.
Muppet Treasure Island, on the other hand, plays fast and loose with the text, with Muppets fighting pirates with ninja starfish, A Latin music style absurdist song sequence & Squire Trelawney thinking a man lives in his finger. The basic story remains the same but there's plenty of new material in there to paint a whole new picture, usually with a comedic twist.
In summation, The Muppets' Christmas Carol is A Christmas Carol movie featuring Muppets, while Muppet Treasure Island is a Muppet movie inspired by Treasure Island.