zoo and zoa are the same thing, people just choosing to truncate Zoanthid differently.
Palythoas are larger zoos. they usually have to be a diameter of larger than a dime at full size. they may also grow on stalks, depending on lighting. then there are Para's (not sure what the full length term is, parathoas, para-palythoas, para-zoas....etc) but these are the largest of the zoanthid type soft corals, almost always having a stalk and usually at least the size of a quarter or more.