Hey we'll give this kid more info than he could ever want.
The AR15 is/was an Armalite-designed rifle that is selective fire in that it could shoot either full auto or semi-auto. The company submitted it first to the Air Force for testing, then the Army got ahold of it. Somewhere along the line, Colt bought the design from Armalite. The Army liked the rifle and adopted it, calling it (for DoD purposes), the M16.
Colt marketed the AR15 in a semi-auto version for sale to civilians, because full auto weapons are either illegal or very hard to get due to government regulation, depending on where you live. So today, generally, the AR15 has come to refer to a semi-auto rifle made by now one of several manufacturers that most of the people on this board can and do own. M16 is the selective fire version of the same rifle (i.e., you can fire it semi or like a machinegun). Very few of the people on this board own one of those, but all would like to . . . [;)]