AR15: the original .223/5.56mm design, of which the M16 and M4 are based on. Early AR15s were select-fire capable (full and semi-auto), but these days AR15s are almost always semi-auto only.
M16: the military's designation of the AR15, which they adopted in 1963-64. Followed by the M16A1, M16A2, M16A3, and M16A4. These are all select-fire cable.
M4: a carbine (short-barreled) version of the AR15/M16. First adopted in the 1990s. Also select-fire capable.
GBB or AEG ?