Hi JJ:)
"Heads or tails?" (when flipping a coin to decide on something) has been a fixed expression for several centuries - it may have been a joke originally, as a lot of coins have the head of a monarch on one side - and the "tail" is the opposite side of the head, so to speak :-D. In German we say Kopf oder Zahl (head or number). Some 网友 have suggested that "tails" came from a coin showing an animal on the opposite side, like a bear or a lion, but I think that is likely apocryphal.
I don't recall every having to specify the side of a coin outside of coin flipping, so I am not sure what would be used then. I think front and back would be understood, as in the "front side of a coin". The technical terms in numismatics are obverse (heads) and reverse (tails).