I believe a mine in the UK is still legally defined as subsurface as per the 1954 act. This is entirely due to the substantial HSE issues related to working in a confined space.
Everything else is a quarry, although many would assert a quarry is a mine anyway. People call a coal quarry a mine to maintain clarity for all concerned.
The original meaning of quarry as a verb is to cut and shape large blocks of stone (from latin), so I would tend to think only that should count as a quarry for purists. Everything else is a mine. It leaves open the tantalising prospect of saying the Bath stone mines are actually quarries, and probably would have been called such by the Romans.
I avoid mines and quarries. Smacks of work or something. Ditto digging.