One is a constitutional right, one is a privilege.
You are simultaneously right and wrong.
The right to keep and bear arms is indeed a right recognized (though not granted) by the constitution. Driving is a privilege, which is what I suppose you’re referring to.
However, this bill is not about respecting or expanding your 2nd Amendment rights. Remember that, because it’s important.
The legislation allows someone who is licensed to carry a handgun—only a handgun!—in one state to receive reciprocity for his license in another state in the same manner that we respect driver’s licenses. It even goes further, by stating that a facially valid document is prima facie proof of licensure. If one lives in a state like Vermont or Alaska that does not require licensing to carry a concealed handgun, then one is also good. So far, it sounds great, right?
Except there is an easy way for a state that wishes to exclude people from this law to do so.
This federal bill is predicated on two things—possession of a valid license to carry from State A and the existence of licensing laws for concealed carry in State B (or, like VT or AK, the absence of a legal prohibition). If New Jersey wants to prevent people from Pennsylvania carrying concealed handguns in Jersey all they have to do is repeal their concealed carry law. Individual states have the right to make and enforce their own laws, and this would effectively prevent the federal bill from having any applicability in their state.
The law also does not remove many of the restrictions on concealed carry in federal law. It does not, for example, allow you to carry into the post office or an IRS building or in fact any building in which federal employees regularly work.
If this were about respecting your 2nd Amendment rights, Congress would simply pass a law saying notwithstanding any state law to the contrary, non-prohibited people possessing commonly recognized identification documents can carry concealed weapons that have been shipped in foreign or interstate commerce without the need for a state license.
But it’s not. This is about extending full faith and credit to a state-issued license. As such, it sets the groundwork for other licenses to be accepted, though it’s likely that this will require enabling legislation or a recognition by the federal judiciary that the public records referred to in Article 4 section 1 include publicly accessible professional licenses. For example, many professional licenses are public records in PA, including every level of healthcare provider.