SPS: small polyped stoney corals such as acropora, montipora, etc.
Clams: maxima, crocea, tridancia
LPS: Large polyped stony corals such as Frogspawn, Torch.
Stony coral is basically a coral having a hard, stone like base.
leathers are softies because they have a soft base you can frag for example.
SPS and clams really need halide light to be healthy and thrive.
SPS are also somewhat harder to keep but it depends.