Here is a longer quote from another site.
First off, anything that fits into the Zoanthidae family is called a zoa (Zoanthus sp., Palythoa sp., Protopalythoa sp., Acrozoanthus sp., etc.). Zoa is the generic term for all. It's when we try to go further into classification that the issues with naming start.
Below is the answer to the difference between zoas and palys, though the vast majority of people don't really care about the differences (most thinik size is what makes it a Zoanthus sp or a Palythoa, but that is rediculous is you've seen more than a few tanks with different lighting schemes...).
Palythoa species take fine grit into their coenenchyme (stalks or mats). Zoanthus sp do not. For years, everyone (myself included) grouped people eater zoas (PE's) in the Protopalythoa genus. Since the Protopalythoa genus is closely related to Palythoa, people started grouping PE's as Paly's. Since PE's were bigger than most zoas, people started to equate anything larger than what they were used to seeing as a Zoanthus a Palythoa. That and the fact that common button polyps are a Paly sp (or Protopalythoa psammaphila) and are larger than the perceived size of most Zoanthus sp has to be where the size-determines-classification came from... I have some of what I think are Palythoa cavernosa that are smaller than most of my Zoanthus sp... Size doesn't matter (may sound better coming from a lady, huh). A zoa researcher (James Reimer) that educated many of us on the differences said he expects Protopalythoa to be removed from classifications once more research is done-he expects it to be absorbed into the Palythoa genus.
This all came from the creation of the new species to incorporate the PE type zoas. Reimer, et al, classified PE's by DNA into the species Zoanthus gigantus. As far as I know, all zoas that have white striping on the underside of the polyp (I think all of which have neone green slit mouths, too) fall into this species.
This is still not a set in stone way to tell the difference, but it makes it a little easier. If the mats and stalks are smooth and don't seem gritty, it is most likely a Zoanthus sp. If it appears to have any grit in the stalks/mats, it is most likely a Palythoa sp. You'll find that the vast majority of people will call anything bigger than a pencil eraser a paly... This makes it difficult for newbies to understand the actual difference (not the hobbyist created difference)...