The M is for mobile version. The 670m and 680m are for laptops and are not as powerful as the desktop 670 and 680.
Side by side comparison of the 670m and 680m I don't know about the 670m, but I do believe I've read from different places that the 680m is comparable to the desktop 570 in terms of performance.
Other than that, all I can tell you is on my 680m on high settings I'm mostly running a smooth 60ish fps. When I try to go to maximum my fps drops to 25-30. If you already have, or are planning to get the 670m, I hope it runs smooth for you and that you enjoy the game.
Edited, Jun 29th 2013 1:14am by Hatamaz