“Navy” does feel like a familiar, real world term. But really, it’s just a generic term for a maritime war force, so any land/world that has armies can also have navies.
When it comes to seeing an army on the show, it’s pretty much always been George’s. Regina’s got her men in black, but we’ve seen George’s troops in full uniform, wearing the family crest and all. Makes me wonder if perhaps the Navy that Liam was in, also belonged to George’s kingdom, so they can keep that theme going of showing military wearing that crest, to tie it all together?
If young Killian is associated with Liam, (either because they’re family, or just because he was a part of his crew), and they were in the Navy that served George’s kingdom, (several generations before George was alive of course), that would be a way back connection for Hook to the present day Charming family, (who inherited the armed forces of George’s kingdom when they took over).