Is it grammatically correct for a pilot or airline cabin crew to say "welcome on board", rather than "welcome aboard?" Is there a difference?
On board describes that something is aboard a vessel i.e., the location of something or someone
Onboard is one word (sometimes hyphenated—on-board) when it comes before the noun it modifies (e.g., onboard radio, onboard computer). Elsewhere, writers usually make on board two words. For instance, one might write, “We brought a radio on board so we could have an onboard radio.” Reference Onbaord vs on board
It's rather an idiomatic phrase (or a quasi-adverb)
Examples: There are no medical physicians on board. Smoking is not allowed on board.
Aboard modifies an action and is often followed by reference of the vessel, e.g. to step aboard a something.
We are on board the plane because we have boarded the aircraft.
Aboard the ship, we watched the waves.
Perhaps a bit silly, but:
As you are now on board, welcome aboard the our vessel.
As you are now aboard (the vessel) let me say welcome on board!
I don't see any grammitical difference, rather it seems to be usage as Fumble (hi ya Fumble :) says. (And there's Amid ship - center of ship.)
It would be even more silly, but grammatically correct, to say:
As you are now aboard, let me say welcome aboard.
I wonder if the word 'board' derives from the planks / boards used from dock to ship to enter the vessel?
"Arrr matey, Howard, walk the plank off board!"