Ok, so.... the answer could be "neither", but also "both", depending on your perspective. As far as I can tell, this looks to me like either a solitary cup coral, or a corallimorph "anemone". In either case, "coral" would probably be the more correct answer. They're both related to stony corals, but they're not colonial and generally don't build calcareous skeletons, at least not in the same way most of the typical scleractinians do. Their common names sometimes refer to them as "anemones" since they look similar.
I can't provide you a species name, since I have no idea where in the US you are, or where you got your live rock from. Also, I'm not as familiar with tropical species in general. It is also possible that it's a very small anemone, but it's hard to say for sure without clearer photos.