Lots of names for the same thing I think...
Mini calls it Camera Based Cruise Control, ACC in the manual and ACC stands for Active Cruise Control in the index. It uses a camera and is part of the driving assistant pack.
The driving assistant pack also includes display of road speed limits based on signs recognised by the camera (and/or info from the sat nav, if fitted). This part seems to be country specific, I suppose because the signs are different.
The speed limit display is distinct from the speed limiter, which is a function of the ordinary cruise control (but that might be country specific as well as it doesn't seem to be described in the US online manual).
It's not surprising that there is some confusion!