Yeah, generally speaking, that is the "deal". Yellower, pale brooksi types can sometimes be found in other parts of Florida, but the paler examples with more crossbars are generally found in extreme south Florida, from where the "brooksi" was first described. The term "brooks" definitely gets very over-used in the hobby, and many normal Florida kings are referred to as "brooks" kings when in fact they are actually Florida kings.
Actually, although the lighter yellow, paler kings are still referred to as brooksi, they are simply a clinal variant form of floridana.
Hobbyists and breeders still use the descriptive term "Brook's king, or "brooksi" to refer to the lighter forms of floridana.
Of course you have the "peninsular" intrgrade kings too from the more central/northern parts too which can add to the confusion as well, and all of them can be variable too depending on the percentages of intergradation involved.
In my opinion, the darker floridana are best referred to as "Florida kings", and the yellower,paler one's referred to as "Brook's kings", but both are indeed true "floridana".
This pair would certainly be considered brooksi, but it is still argued by some that the less defined patterned individuals more typical of the phenotype from extreme south Florida be the only ones referred to as Brook's kings.
~Doug
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"a snake in the grass is a GOOD thing" 
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