here I'll try and lay it out straight if I can they all fall under the family Zoanthidae
then are sperated into four Genus, Zoanthus, Palythoa, Protopalythoa, Isaurus.
then seperated into individual species wich i'm not going to list as there are too many to conviniently type out.
there is research showing that the two genus Palythoa and protopalythoa may actually be one genus Palythoa BUT tazxonomic troubles never end. for now I am going to stick to calling them seperately untill I see more research on the matter.
Zoa and zoanthid are technically all four genus, but most people are refferring to zoanthus when they say Zoa or zoo. paly is just palythoa or protopalythoa, and isaurus are rarely seen in the hobby though slowly getting around.