What is the main difference between A2 and A3 sights?

The A2 and the A3 sights are identical in operation and items:Peep sight diameter,same elevation and windage adjustments. The only difference is that the A2 sights are on the standard fixed carrying handle receiver and the A3 is on the removable handle that goes on the flattop receivers.

that seems to be what it has become, but i dont think it was originally like that.  the m16a2 and the m16a3 have the same sights as far as i know, just the a3 is full auto and the a2 is burst.  (but in general, you do indeed hear people refering to the detachable carry handles as a3 sights)

Detachable carry handle sights (late M4 and M4A1 carbines, M16A4) have a different thread pattern and only go up to 600 meters in "half click" stops.

They're otherwise the same.  Wheel is marked 6/3 rather than 8/3 to show the max adjustment.

Civilian makers can't decide if flattops are A3 or A4 and I've seen "M4A3" Carbines avertised, whatever they might be.  All but the very first M4 carbines have detachable handles.

-- Chuck