i thought it was the same thing
similar but not the same. AC cable can use the sheath as an EGC due to the bonding wire that runs inside the metal sheath. Due to that, it does not have to have a separate egc within. MC sheath is not an acceptable egc but it can be purchased with an egc (such as I see yours has).
There is a difference in the material used to wrap the conductors as well. If I remember correctly, MC uses a paper wrap and AC uses a plastic wrap. Not sure of that and it may have changed since the last I worked with it.
so, does your code spec AC specifically?
regardless of which you use, be sure you use the proper connectors. There are some that can be used with either but there are also some that are listed for use with just one or the other.
also, one requires the use of the red insulators in the end of the sheath and the other doesn't (although most people I know use them in either). It's late and offhand I cannot recall which requires the insulators and which one doesn't.