Okay. Here's the skinny. You have to know I would chime in...
Back before a guy named James Reimer (a zoa researcher in Japan or Okinawa) turned my loose zoa ID'ing life upside down with an actual classification for PE's, we used to call all large polyped zoas Protopalythoa. At that time, all PE's, as well as the millions of morphs that may look similar to the green Protopalythoa psammaphila above in Brian's shot, were lumped into this category. The only thing that was ever considered a paly by me (so many people call things paly's when they aren't, esp. in the Zoa forum) was the picture below.
http://www.advancedaquarist.com/issues/feb2003/Palythoaorange.htm
In this pic, the mouths are mostly closed, but that allows you to see the structure. A classical Palythoa (by the majority of us who had actually looked into it before jreimer changed things) was thought of as a thick mat with an embedded coenenchyme (stalk). The mouths were at or very near the surface of the mat. You see tons of these in the Caribbean, but don't see them for sale as much, as colors are limited.
What was left over were usually refered to as zoas, though there are a number of other genus of zoanthids. FWIW, zoa(nthid) is a generic term including all similar genus. Zoanthus is a genus, Palythoa is a genus, and (currently) Protopalythoa is a genus.
Fast forward...
James Reimer did a DNA analysis on several similar morphs of zoas to classify them. It just so happened that the ones he tested were RPE's (red people eaters). He conclusively showed that all zoas that have the white striations on the underside of the polyp when it is closed and the green slit mouth are Zoanthus gigantus. I have seen one of his photo albums online and he has other zoas besides PE's in his Z. gigantus album. I will hunt that link down and post a little later.
In addition to the reclassification, he helped further educate some of us in the zoa forum on Palythoa's. He mentioned that the genus Protopalythoa will most likely be absorbed into the Palythoa genus. What makes something a Palythoa is that the animal takes fine particles (sand, etc.) into its coenenchyme. In Brian's Protopalythoa psammaphila above, if you look closely, you can see what looks like fine sand paper. That supports the paly description and his statment that Proto. will likely be absorbed, as the genetic similarities are too similar to need a separate genus in many cases. There are still a lot of unknowns, as this is not a hot spot for scientists. People like James Reimer will eventually research these guys and classify them all (may take several lifetimes, but any advancements are nice).
All that said, here is a link that I have posted in the Zoa forum several times over the years with some shots of different types of zoas (and descriptions). Bear in mind that some of this info may be outdated, but most of it is still current with today's research.
http://www.advancedaquarist.com/issues/feb2003/invert.htm