AC Schnitzer is just a tuner. They don't sell cars like Alpina does. What tells you that you have an ACS 325i?
ACS makes all kinds of accesories for BMWs. WHat your car has on it depends exclusively on what ACS mods the previous owner(s) have put on the car. The body kit would be an obvious one, but you may have a short shifter, exhaust, or any of several other things.
I wouldn't call your car an ACS BMW. I would call it a BMW with ACS mods.
Welcome to BMW ownership, by the way