M4A1 is a Carbine.
The entire M4 nomenclature is a carbine version of the M16 seriers.
I believe the A1 and A2 desigators are for 1 being fully automatic (A-1 MW version), The A2 is what is standard issue in the army, 3 -round burst. I am an officer in the Army and I do not know of any units that are actually issued the Fully Auto version. However, I am sure Special Forces and such have the option to get it (they get pretty much whatever they want)
I am friends with some Rangers, and they were not issued A-1s, I am sure the reason IW choose the A1 was to make it more distict from the M16 A4
End of 2009 Predictions (Set, January 1st 2009)
Wii- 72 million 3rd Year Peak, better slate of releases
360- 37 million Should trend down slightly after 3rd year peak
PS3- 29 million Sales should pick up next year, 3rd year peak and price cut