The key portion of the statute states that it applies to the discharge of a firearm:
in any public place or on the right-of-way of any paved public road,
highway, or street, who knowingly discharges any firearm over the
right-of-way of any paved public road, highway, or street or over any
occupied premises, or who recklessly or negligently discharges a
firearm outdoors on any property used primarily as the site of a
dwelling as defined in s. 776.013 or zoned exclusively for residential
use commits a misdemeanor of the first degree, punishable as provided
in s. 775.082 or s. 775.083. This section does not apply to a person
lawfully defending life or property or performing official duties
requiring the discharge of a firearm or to a person discharging a
firearm on public roads or properties expressly approved for hunting
by the Fish and Wildlife Conservation Commission or Florida Forest
Assuming that the permitted hunting approval exception does not apply in all cases, it would not be directly applicable in a federal park (where federal courts probably have exclusive jurisdiction), although there is probably an assimilative crimes act that adopts state law as a federal criminal offense in cases not provided for by express federal statutes that would apply as if it were state land.
So, you can't discharge a firearm "in any public place", over a paved road, over an occupied building, on a residential lot, or in a residential lot (other subsections limit firing guns from our vehicle).
It appears that "in a public place" is a question of fact, but that would not be synonymous with, land owned by the government. Instead, it would be in places where members of the public gather such as courtyards, malls, plazas, parking lots and the like. Some places in Everglades National Park or public lands would be "in a public place", but that wouldn't necessarily apply to all places on government owned land. A secluded meadow or bare place in the marsh might not be "in a public place."
Private land would usually not be "a public place" although a mall or amusement park or concert venue or other place open to the public but privately owned probably would be "a public place."
A paved private road would probably be covered, as would any residentially zoned land and any land in the curtilage of a home or occupied building.
But, otherwise, shooting on private land (not from a vehicle) would be permitted whether it was vacant land, farm land, industrial property, or commercial property without occupied structures or paved roads (e.g. warehouses or storage sheds).