There are over 20 different species of bubblenesting bettas alone not counting the subspecies.
Most all of what we see here in the United States are variants on the
Betta splendens (i.e. Halfmoon, Crowntail, Veiltail, Delta, Super Delta, Doubletail)....I am sure that is what he was referring to and it refers to the body shape and the type of fins that the fish has.
I will show you pictures of my Crowntail and Halfmoon males and Veiltail male to show you some of the differences.
The first picture is of the Crowntail, Marty (blue/white)
The next picture is of the Halfmoon, Alexander (blue)
The third is the Veiltail male, Azul. (turquoise)
Hope this helps.
Rose
p.s. as far as the females being smaller and not as colorful, do be careful as they are being bred to be more beautiful so they will sell better. The fourth picture is my female Halfmoon and while she is not a fishstore female she is getting to be what will soon be the more normal female.