The M16 and AR15 are identical in every way except one small piece of metal in the fire control group, which controls the number of rounds fed with each pull of the trigger.
The original M16 and M16-A1 offered three options on the safety switch: safe, semi-automatic, and fully-automatic. Since soldiers wasted too much ammunition on full-auto mode, the post-Vietnam M16's (M16-A2 and M16-A3) were limited to safe, semi-auto, and three-round burst.
The AR15 only has two modes, safe and semi-automatic. The firearm is in all other ways identical to the M16 produced for the military.
That being said, there are a lot of differences between various AR platforms (AR10, AR15, M4, M16, etc). It's an extremely versatile platform that can be used for everything from long-range sniping to close-quarters combat. Here are two AR's that are on opposite ends of the spectrum...
An AR-15 pistol. I think these things are extremely ugly, but I'm sure some people love them.
An AR-15 in a standard combat configuration with a grenade launcher. That's a thing of beauty...
This AR-15 has been converted to a sniper platform. It has a 24" barrel, a flat-top receiver (no carrying handle), a decent scope, and has been chambered for .308 instead of .223.
All three weapons are based on the same receiver, but each one has been tweaked to an incredible degree to suit the exact requirements of their owners. The military does the same thing. They've got a basic M16/M4 they offer to most soldiers, and a bunch of highly individualized weapons they offer to snipers, urban combatants, and tank drivers/gunners, and other special groups.
-b0b
(...the more you know!)