A concealed carry permit is a right to possess a firearm within a state that issues one. It is not a right to possess a firearm everywhere, which is beyond the jurisdiction of a state government to do.
In the same way, a license to practice medicine in one state is not a licenses to practice medicine in another state.
Reciprocal driver's license recognition is not a function of the full faith and credit clause of the constitution. It is statutory.
Marriage is a legal status of a person, which is a different from a right to do something in a state.