Perhaps... because the american version and the english one had to be different. If one was multiplayer, the other needed another name. And the game was based on fights so... arena was a good word. O that's what I think.
The PC versions of both are nearly identical (nearly meaning the name changes and such) as well as the PlayStation2 versions, though the Xbox and GameCube versions had to go through some more development because there wasn't a Rayman M for Xbox or GameCube. I personally prefer the Rayman M-like versions (PC; PlayStation2) because I really didn't like the changes. Because of a new menu layout, 3 opponent fights in Single-Player were gone, there was this auto-aim system that could be used (could, thankfully; it really isn't that efficient to begin with, plus the fact that manually aiming is funner in my opinion), it still retained some clunkiness, and a few other things. Just wasn't as fun, even with the added stuff. Be glad with Rayman M. (If you Europeans are really wanting to try and have a GameCube, you could buy the Freeloader PAL GameCube disc that allows you to play GameCube games from any region and import Rayman Arena.)
You really don't need Rayman M with Rayman Arena on hand. (I forgot that Rayman Arena for PC had the LAN play that Rayman M didn't have, though Ubisoft finally decided to ready the mode in 2006. Other than that, there aren't any notable differences.)
Hum... I remember that, when Rayman M appeared in Spain, I was sad because I hadn't got the Playstation 2... but then I saw Rayman Rush. Is quite similar to RM and RA but for Playstation 1 and withouth the fights levels.