Funny - I'd never thought of a connection between the two before, but I see what you're getting at. Sometimes it's hard to ascribe a relationship when the tunes are just different enough, and for me, these two are. But this isn't so much a matter of right and wrong, especially when documentation to clear the issue will never be had in the case of old or otherwise unascribed tunes. Sometimes it's just in how you hear things.
Melodically the two tunes seem to broadly have some things in common, but there are crucial differences in the directions those melodies go at certain points when you line them up side by side, so consequently I hear those tunes as harmonically different from each other, and for me that lends additional weight in marking differences that are important for me; for an easy example (presuming we're playing it in G), despite their superficial similarities, the B section of O'Sullivan's March begins fundamentally in the key of C for me, but to me Out On The Ocean's B section starts out in Em. Of course, others may hear it differently, and taking license with what chords you choose to play for the sake of performance is another matter too. Such room for variance allows us to speculate that one melody could have somehow inspired the other, but for me the end results are very divergent despite the melodic similarities they might have, which also raises the rather thin possibility that each could have been composed in isolation. I think it's fair to observe that these two tunes show some degree of familial relationship in their general composition, but that isn't to say that one was necessarily directly inspired by the other. By the same token, maybe they were. But that's lost in the mists of time.
Bear in mind that if you think of a musical tradition as a "language", there will always be recurring elements, combinations, and themes specific to it that make it identifiably what it is, and these things in their similarities are bound to pop up again and again; it's in how you combine them that the differences are made. Just don't get the two mixed up if you play one after the other. On the other hand, maybe it won't matter if you do - you know the old joke: Irish music is all just the same tune.

What I think is good is that you're actually
listening to and weighing these things, whatever you determine of them.
