They are both AR15s. AR15 is a broad term used to refer to the family of rifles based on the design of Eugene Stoner. The alpha numerical designations refer to the specific features of that model. The A4 is the same as the A2 in that it has 3 round burst, but with a detachable carry handle to allow mounting of optics. The A2 is a fixed carry handle to which adding optics is not as practical. The M16A3 is the same as the A4 only with a full auto setting in place of the 3 round burst.
It appears to me that you are referring to an M4, not an A4. A4 (and in some cases A3) generally refers to current generation FLAT TOP AR15's. A2 is the standard, fixed carry handle model. No AR15 should have 3 burst capability and still be referred to as an AR15. That would make it a military/police M4 or M16.
I was going to have to disagree with first answer also...
An 'A4' is a military aircraft.
An AR-15 is a civilian version of a military issued rife.
Later Variations of the M-16 were designated as 'M-16A1', 'M-16A2', 'M-16A3', M-16A4', ect.
What the OP was probably trying to ask was about the difference between the current production versions of the AR-15 and the military issued M-16A4,
The OP was trying to ask about the 'M-4' military carbine.