They are both pretty similar, here are a few articles I found about the differences. I think everyone used to say that the difference was that one was connected by a rubbery mat, while the other was not. However, these articles seem to disagree, one article says that both are connected by a rubbery mat. Also, one article says that zoas just need light, while palys will eat meaty foods as well. Also, plays tend to have shorter skirts, almost just nubs, as opposed to zoas which have longer skirts. Still, pretty interesting reading.
And as Trido says, I think Palys tend to be larger, I think one of the articles says the same thing.
Here is what the first article says about them, you can see that they are only distinguished from one another at the Genus level, so they are in the same phylum, class, subclass, order, and possibly family. Hope someone else chimes in if I am wrong!
Phylum: cnidaria
Class: Anthozoa (anemones and corals)
Subclass: Zoatharia
Order: Zoanthidea (Zoanthids)
Family(s): Parazoanthus (Yellow polyps), Epizoanthis ( Brown to red brown colonial polyp disks - medium tentacles ), Zoanthdae (Hexacorallia)
Genu(s): Isaurus , Palythoa (larger than Zoanthus with longer brown tentacles. May be bright green in center, common name is Paly)
Zoanthus (small colonial polyps - green, red, brown, blue, purple, yellow and a range of other colors. Central disk may be contrasting color. Polyps connected at base)
Specie(s): Zoanthus alderi, Zoanthus kealakekuaensis, Zoanthus pacificus, Zoanthus pulchellus (Caribbean and found mainly on offshore), Zoanthus sociatus (green sea mat from Caribbean)
The Zoanthids we commonly keep in our aquariums belong to the genera of Zoanthus and Palythoa however we may actually have corals in the Zoanthdae family in the genus of Zoanthus, Protopalythoa, Palythoa, Isaurus, and Acrozoanthus.
http://www.salt-city.org/showthread.php?t=11186
http://www.advancedaquarist.com/issues/feb2003/invert.htm
http://www.saltcorner.com/sections/guest/fatherree/Zoanthids.htm