"On board" suggests something/ someone is on a vehicle or vessel. But "abroad" will mean someone (usually "someone" and not "something") is overseas.
(Edit: Rick just pointed out my explanation is wrong. I'll leave the incorrect bit for other viewers).
The correct one should be: There is is no real difference in the meaning, but it shows itself in different sentence structures. However, they aren't used interchangeably.
a) On board: Something/ someone is on a vessel/ vehicle. Example: "There are three passengers on board."
b) Aboard: Also means the same thing, but is the adverb to the verb "to board". "There are three passengers aboard the ship."