"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.