I'll give it a shot, but I agree that it's confusing. I've asked the same type of question before - right here in the forum. Here's how I understand it now:
As far as taxonomists are concerned, there are currently only two recognized subspecies involved here: the Eastern King (L. g. getula) and the Florida King (L. g. floridiana). There are two types of recognized relict intergrades (L. g. getula X L. g. floridiana): the Peninsula intergrade, generally found across the northern, central, and eastern Florida peninsula, and the Blotched (or sometimes Apalachicola Lowland) intergrade, which is found in the Apalachicola Peninsula region of the central Florida panhandle. (The Outer Banks Kingsnake, found in the N. Carolina coastal regions, also might be a third relict form of Eastern/Florida intergrade.)
Herp enthusiasts, however, often refer to Florida Kings as "Brooksis" and Blotched (intergrade) Kings as "Goinis." The reason is that the Blotched Kingsnake was once considered a separate subspecies by taxonomists, and was given the taxonomic name L. g. goini. Also, taxonomists once considered the Peninsula Intergrade to be it's own separate subspecies. They originially gave IT the name L. g. floridiana, and called the lighter subspecies, found in the southern Florida peninsula, the name L. g. brooksi. They have since determined that both L. g. goini and L. g. floridiana are actually relict intergrades. So they eliminated those classifications, and changed the classification of L. g. brooksi to L. g. floridiana. But old habits are hard to break, and hobbyists still refer to the blotched intergrade as "goini" and the Florida King as "Brooksi."
To summarize:
L. g. getula (Eastern King) is unchanged.
L. g. brooksi is now L. g. floridiana (Florida King).
(former) L. g. floridiana is now the Peninsula intergrade.
L. g. goini is now the Blotched intergrade.
L. g. brooksi and L. g. goini are no longer recognized by taxonomists as separate subspecies.
I hope this helps. If not, I'll defer to Keith Hillson (who I'd consider the authority on Eastern Kings) or some of the other regulars here who are quite knowledgable.
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MichaelB