Actually, there is a difference in the original sources:
triakontoros (τριακόντορος)- ship with 30 oars
triakonteres (τριακοντήρης) - ship with 30 rowers per oar.
Both names are basically the Greek for 'thirty' (triakonta) with an ending added, but it's a different ending. -ros for a ship with that number of oars, -res for one with that number of rowers per bench. (plus the preceding vowel changes.)
The problem is that in English we tend to knock off the -os or -es ending, making the two words indistinguishable. For what it's worth I've seen the word 'pentekontor' or 'pentekonter' (both spellings are used) in English texts to describe the type of galley with a single row of oars, 25 per side, used during the Homeric era and the siege of Troy.
We don't have detailed descriptions of how polyremes worked, but modern historians believe that the larger galleys had at most three banks of oars, with multiple oarsmen on some of them. Pentereis (quinqueremes), for example, probably had three rows of oars with one man on the top one and two on each of the lower pairs. The really huge ships like the thirties more likely had just one huge oar with thirty people pulling it. Bear in mind that the biggest ships were mostly one-off vanity projects by Alexander's successors, so it wasn't as if these were "real words" in Greek. It's more the other way around; if Ptolemy the Whateverth announced he was building a ship with 137 rowers per oar, then writers would make up the word "137-er" to describe it.