After looking it up, beef/other meat mince can refer to meat that has been passed through a grinder.

This product is distinguished from ground meat in the same jurisdictions by the fact that mince cannot be comprised of anything other than the cut of meat that was put into the grinder. Ground meat, on the other hand, can have additional fat or ice/water added to adjust the texture.

(Naturally mince can still refer to very finely chopped meat as well, but in many places it refers to the unadulterated ground cuts.)