=Small Polyped Stoney--Hard corals that have small polyps on a hard skeleton and they usually come in branch or plate type species.
=Large Polyps Stoney--Also with hard skeletons but usually have larger fleshier polyps. LPS
tend to grow faster and larger for the most part.
Both are hard corals.
This is as basic as it can get for a definition, if you would like more information, ask away.
Soft corals do not have a hard skeleton, therefore not usually requiring as much calcium to grow. Ex are leather, finger, tree, are soft corals. Some also classify zoos/polyps/ricordia-schrooms into the soft category or they may be in a category of their own but are soft corals.