The answer is that they are or were almost the same cat but the Ragdoll has to be pointed with blue eyes while the RagaMuffin can be in a wide range of coat types and is not restricted to the pointed coat. Although the Ragdoll is pointed some varieties have white fur within the pointing.
There are also differences in the breed standards (but they are written in a different style making comparison impossible). The differences are due to outcrossing to other breeds with respect to the RagaMuffin leading to fairly fairly slight differences in overall appearance; for example in the shape of the top of head but I would doubt if people will see that much difference in body conformation. Both cats are substantial in size.
If you hover the mouse over the slide show a pause button shows at the top.
The reason for the similarity is because of the history of the Ragdoll cat. The original RagaMuffin cat breeders were Ragdoll breeders who decided to go their own way because of differences of opinion. It seems that the Californian founder of the Ragdoll cat imposed restrictions and demands that some breeders within the Ragdoll franchise (IRCA) found unacceptable.
The exact date of the split is in dispute but is said to be in the 1980s. The splinter group renamed their breed RagaMuffin and their first cats were descended from Ragdolls. They bred the Ragdolls to Persians, pointed Persians and other Ragdolls bringing in traditional colors such as torties, tabbies and solid colors.
I hope that explains the differences between the Ragdoll and RagaMuffin cats. The slide show above shows some prime examples of both breeds.