I believe that in FL it is just the original certificate with a notation that shows your new name and sex in addition to your original data.
I used to think that those of us born in Texas had it bad, but, unfortunately, FL seems to be worse.
I switched my driver's license to FL yesterday, and the DMV lady (in Orlando) really was quite clueless, asking for a gender change letter because the new name/sex was different from my license from 20 years ago. I had to talk to another DMV agent, who finally understood that I don't need a gender change letter if my valid out of state license, SSA records and birth certificate all now identify me as female. *sigh*