What is the difference between jump rope and skipping?

Neither is right or wrong, they’re both the same. It just depends on where you’re from and whom you speak to. Skipping rope is very common in European countries whereas jump rope is more common in the USA and Asian countries.

Both can be used as both a verb and a noun. ‘Rope jumping’, ‘rope skipping’, ‘jumping rope’ and simply ‘skipping’ are all commonplace verbs for using a skipping/jump rope.

Both ‘jump rope’ and ‘skipping’ are internationally-used terms for the sport we all know and love. The beautiful thing about language is how diverse and colourful it can be. Even closely-related related languages such as British and American English can have wildly different names for things.