As others have said, for me it's the difference between Star Trek (albeit Star Trek with Treasure Planet aesthetic/tech) and Pirates of the Caribbean.
Both can be absolute gobs of fun, and I don't even think tone is that important to either; either genre can do horror, suspense, comedy, thrill and action adventure. But I think in terms of genre, they actually do fit different niches.
A sea campaign is always going to be a bit more grounded (no pun intended). Yes you can go from island to island, and each island is going to be very different... but there is an expectation that the sea is not limitless, and even if you're exploring these islands for the first time, someone can always follow you. Eventually, you'll run out of sea to sail, and even if that can last a campaign for years, I think there should be an expectation from the characters that the journey can't go one forever, that there is an end-goal in sight.
A great example of this... is One Piece! This is literally a pirate campaign that has gone on for years, and who knows when/if it will end. However, the characters of One Piece (the strawhat crew) have a tangible goal in sight; to recreate the journey of the Pirate King, Gol D. Roger, find his treasure and become the new Pirate King. Even if the adventure never actually ends and they just keep visiting new island after island, there is an expectation of getting closer to that goal, the challenges and adversaries they face escalating as they get closer to achieving the mantle of Pirate King. This all makes sense; despite being a huge world with seemingly hundreds of islands, the world is finite and doesn't go one forever. And institutions in the world reflect that, with some waiting for the Strawhats at the end (The Four Pirate Emperors) and other pursuing them (The World Government and Marines).
I don't believe that same expectation, that the world is finite and "the adventure eventually ends" really applies to Spelljammer. The Astral Sea is for all intensive purposes, limitless. And much like TOS Star Trek, there isn't really an expectation that the goal can ever be completed; it's just to explore new worlds. And there are always new worlds! I know the show says "It's five-year mission" but there's technically no reason it has to be five years; it can go on forever, and it kind of does (although the person in the captain's chair changes). And I think that does fit a different genre in some ways; you don't really need an "end" as much as a sea campaign does.
That said, you can mostly do the same tropes in either. And obviously, the biggest difference is aesthetic; one is in space, the other is on water. Some folks prefer one or the other.