read bettysplenden.com ; Betta Splendens - Half Moon, Double Tail, Crown Tail Bettas - Welcome
and bettaterritory - all about betta section ; AAB
In short, the VT was a mutation from the PK which was then bred for long their fins.
As best as I can remember, the first "modern" fin type was the HM which was created from wide VT. I'm guessing they kept crossing VT to DT and kept breeding the widest fin spread until the mutation appeared.
Most bettas carries CT gene to a certain extent. This can be viewed from the spikes at the end of the fins. In my area they are call "the gear effect". Some of you call them comb tails. These were constantly bred to then create the CT mutation.
Later breeders crossed HM to PK (and other fin types) and created the so called HMPK. Initially this was done mainly to thicken the HM's fins. But eventually HMPK became popular and was accepted in the IBC.
I don't exactly remember the details.
And if' you're wondering about modern colors - metallic and dragon; they are results from crossing splendens to mahachai and smaragdina (wild type) which increased the metallic color.
Btw, welcome to the forum.