Below are the functions of each drill.
Hammer Drill -This term generally refers to impact type drills. It works like a drill except that a set of ratchets, one turning on the spindle & the other fixed in the housing, bounces against each other giving a forward thrust to the bit & allowing it to pulverize the concrete. These products generally hit about 1/10th as hard as a rotary hammer but they hit about 10 times faster.
Hammer - The motor drives the piston forward, causing high air pressure between the piston & the ram. The air pressure builds to the point where it fires the ram forward into the beat piece, which in turn hits the back end of the bit. The ram bounces back and the cycle repeats itself. A hammer works best when only light pressure is applied.
Rotary Hammer - Uses the same theory as the hammer, however a rotary hammer adds a gear train to rotate the bit as it impacts. Unlike a hammer drill, the blow delivered is entirely dependent on the mechanism, so pushing harder won't cause it to drill faster.