Did the Rancor follow Luke from the

No, that was a different monster. The fandom wiki calls it a dragonsnake: https://starwars.fandom.com/wiki/Dragonsnake

In the SNES game of Empire Strikes Back, the boss of the Dagobah levels is Habogad (Dagobah backwards), and I think that it's meant to be the dragonsnake. https://starwars.fandom.com/wiki/Habogad

Truthfully, we never really see what the thing is in the film, as you pointed out, but given that it lurks under water, it seems unlikely that it's the rancor, which has no visible advantages for swimming.