I've been collecting, growing, and talking about cycads for almost twenty years now, but I still really don't get it. I've read the exact scientific explanations and it just seems to make it worse, so here's what I know:
Under the main category of cycads are these that I have here at The Tropical Paradise are:
The most common cycad is a "sago palm", which is a cycas revoluta. Using the common name is pretty safe here, but if you're just starting out collecting, I would recommend that you get into the habit of calling it a cycas revoluta. Collectors usually just call this beautiful plant (somewhat scornfully in my opinion) a revoluta. You can buy these at Home Depot, Walmart, just about anywhere. They grow great in Phoenix and are the least expensive cycad that you can buy.
Slightly rarer in the cycad collecting world are the dioons. Here at The Tropical Paradise I have several dioon edules. To make things even a bit more complicated, I have several that are a particular variety, called dioon edule, var. palma sola. Cycad collectors just say, "palma sola". The other dioons that I have are dioon spinulosums, which have much broader leaves.
Another type of cycad that does well here is the zamia. Of this type of cycad, I have zamia furfuracea (sometimes called a cardboard palm) which has a thick, wide leaf that looks as if it were made out of, well, cardboard, and a zamia floridana (sometimes called a "coontie", but really only in Florida), which has a very fine leaf.
The rarest cycads here at The Tropical Paradise are Encepharlartos. They were all given to me as tiny plants by fellow collectors, and are the ones that can be worth thousands of dollars. But really only for the really, really big ones, and the really, really rare ones, which I don't have.
There, now go practice your Latin!
Pictured: Dioon edule