The term "M16" is the military designation. "AR-15" was Armalite's model designation for the original rifle that was full auto. Later the term "AR-15" came to mean, to most people, the semiauto civilian version.
As far as the actual differences:
First, there is the famous "third hole", drilled directly above the selector hole. This is for the pivot pin for the "autosear". The autosear, in full auto mode, holds the hammer back until the bolt is in full battery, and as the bolt carrier comes all the way forward, the lower rear part of the bolt carrier hits the top of the autosear. The autosear pivots, and the lower part releases the hammer.
The hammer has a spur on the "tail" which catches on the autosear. This spur is ground off on the hammer in the semiauto AR-15.
The safety selector on the AR-15 is simply a cylinder with a flat spot that either holds the rear of the trigger down, in SAFE, or the flat allows the trigger to move in the FIRE position. The M16's selector has some more bumps and warts.
The autosear also has a little arm that comes down and touches the selector. In the Semi postion, the selector touches the arm of the autosear in such a way as to move it so it is disabled, and does not touch the hammer. In the Auto position it allows the autosear to work.
The trigger of the M16 has the slot for the disconnector cut all the way to the rear. The disconnector has a tail that goes out the back of the trigger through this slot, and touches the bottom of the selector. In the Semi postion the disconnector is allowed to move and works like it does on a semiauto AR-15. In the Auto position, a bump on the selector holds the tail of the disconnector down so it does not work.
So, the parts that are different are the selector, the disconnector, the trigger, the hammer, and the bolt carrier. The bolt carrier has more metal on bottom to actuate the autosear. This is cut away area prevents an AR-15 bolt carrier from touching an autosear.
The inside of the lower receiver is made narrower to prevent simply drilling a hole and putting in an autosear. Extra metal would have to be machined out. Some receivers have even more material to prevent "Drop In Auto Sears" from being used. Colt adds a steel block.
So, there you are, the differences between the M16 and AR-15. The semiauto AR-15's lower receivers and fire control parts are designed to prevent use of full auto parts or modification of parts to full auto config.
Edited to add: So, when you hear "All you gotta do to make it full auto is file down the (fill in the blank)", you can call BS on them.