i imagine that the axe was a useful shipboard weapon/tool since it's inception in the start of the age of metals and likely before. as fire is a classical sea weapon, a tool for cutting grappling hook lines, netting, rigging, shifting broken timbers, masts, spars, booms etc. is very useful. a spiked axe is not only such a tool, but makes a handy weapon. maybe not quite as good as a pike or hanger, but a lot better than nothing, especially if you know how to use it. not surprising that fire axes would be very similar if not almost identical. roman legions used a spike axe (dolabra*), i'd guess the roman navy & marines would also. seeing a spike axe in a military vessel would thus have been normal for millenia.
the roman dolabra that follows, if it was a bit more ravaged by time would look much like the axe posted earlier.
dolabra on trajan's column, rome from 113 a.d.: