Welcome on board vs Welcome aboard

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.

"aboard" is only a contraction of "on board". May be pilots prefer "on board", but actually there is no difference between the two variants.

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!"