Whatever the name, there is now a movement sweeping the country to create a procedure to confiscate firearms of suspected at risk individuals before they perpetuate gun violence. Some people refer to these as Red Flag Laws or Gun Violence Restraining Orders/Injunctions.
Carrying a concealed firearm is a felony criminal offense in Florida with several exceptions that almost eat the rule. All of the exceptions, of course, require that the person is not otherwise prohibited from carrying a firearm concealed or otherwise. For example, the exceptions do not apply to people who have an active domestic violence injunction, are on probation, or are a convicted felon.
In criminal cases, searches resulting from vehicle stops have been hotly litigated since the automobile became available to the public in mass. Since cars are mobile and not as private as your home, the Supreme Court has interpreted the constitution to afford vehicle searches and seizures less protection.