AR15 vs M4A1
 

What are the primary differences between an AR15 and a M4A1?

Well, which AR15 would help. Mainly the semi-auto and Full auto capability.

Outside of having the rifle be an SBR and paying the tax, the AR15 would be no shorter than 16 inches, and a real M4 is usually 14 inches, or sometimes 11.5 inches.

That is the baiscs. The M4 has a particular barrel profile, but you can order that as well for you AR15.

Military wise:

M16: 3 round burst, 20" barrel, fixed A2 stock, different barrel profile.
M4: full auto, 14.5" barrel, collapsible stock, M4 barrel profile for the attachment of an M203.

Civilian world nothing other than barrel length, gas system and stock.

An M4A1 is an AR15, but an AR15 may or may not be an M4A1.

Only in the broadest sense...
I sure don't include an M-4 as an AR-15...

AR-15 is a semi-automatic civilian rifle that was occasionally used by the military in the mid 60's.
The AR-15 was designed to fire the .223 Remington round.

An M-4 is a purpose designed & built military weapon.
It is fully automatic. It has fundamental design changes away from the AR-15 format.
It fires the Military/NATO 5.56x45mm round
(and shouldn't be confused with the civilian .223 Remington round).

The M-4 shares less with it's design parent, the AR-15, than any variant to date, and should not be confused with the old standard AR-15.