Things may have changed from when I was in Florida but, ten years ago, a "card" would have been a journeymans license. The electrical contractor would need a master in order to pull the permit, but, anyone doing work under that permit would need to have a journeymans license, or be working under the direct supervision of a licensed journeyman.
I was in Broward county and things may be different where you are but, I remember having to study my ass off twice in order to pass that 6 hour long block exam offered in the Plantation High School cafeteria.
When I was there, the local Ft. Laud. inspectors didn't seem to bother with checking licenses because the county, not the city, would get the money from the fines and why should the city put forth man hours with nothing in return?
Here in Michigan, the state has taken over the testing and licensing of journeyman instead of the local municipalities, and there are laws on the books that would punish those working in the trade without a license just as if we were lawyers, doctors, beauticians etc.
In michigan, and as I recall in Broward county Fl. when I lived there, we were required by law to have our journeymans license on us at all times when working in the field. I still have my framed journeymans license from when I lived down there. If I wouldn't run the risk of waking my new son at 2:00am by getting it out of his closet, I'd take another look at it.
I was sure it was a Florida state license but, I've been wrong before. It's possible it was only a county issued thing.
I'll take a look tomorrow.