If the other party is also a MD resident, and you have no reason to believe that the person is prohibited from buying a firearm under federal law, it is solely a matter of MD state law.
If the buyer is a resident of another state, the handgun transfer must
go through a FFL located in the buyer's state of residence. In this case, the handgun obviously must be legal to own in the destination state.
FFL transfers of this type are generally most easily accomplished if the seller meets the buyer at the FFL's premises in the destination state. Many FFLs near state borders can readily explain the procedures for such transfers. Shipping a handgun is a separate and complicated topic that I don't want to address here.