Section 790.25 is self-contradictory on this point but has generally been held to cover open and concealed.Not concealed... Open carry only, to and from range, fishing, hunting, etc.
On the one hand 790.25(2) says:
This section does not authorize carrying a concealed weapon without a permit, as prohibited by ss. 790.01 and 790.02.
[Note that when it says "this section" it is referring to the entirety of F.S. 790.25.]
But then in the very next subsection, F.S. 790.25(3), it says:
The provisions of ss. 790.053 and 790.06 do not apply in the following instances, and, despite such sections, it is lawful for the following persons to own, possess, and lawfully use firearms and other weapons, ammunition, and supplies for lawful purposes[...]
The courts have generally held that the only reasonable meaning of stating that 790.06 does not apply would be to allow concealed carry.
All of that said, personally I wouldn't carry a firearm concealed without a CWFL under any of the exemptions because the risk is too high. If you are arrested for it and somehow get convicted it's a felony.
Nonetheless it is VERY well settled that you can carry openly or concealed, without a license, at your home or place of business (see Florida Supreme Court ruling in Peoples v State) and all of the other exemptions including camping, fishing, etc. are in the same subsection as "home or place of business".