Considering that the live rock came from the Caribbean and the red seaweed feels geleteous and is slippery to the touch; Halamenia is most likely.
https://www.marineplantbook.com/mar...ies of Halymenia,bottom by a single holdfast.
Know this: Halymenia species are often called Dragons Breath/Dragons Tongue/Red Sea Lettuce
Perhaps if you took a picture of both red seaweeds in LFS that sold you the rock. Then we might move past generic names.
Who knows, the LFS may have two seperate species of Halymenia.
