Since the Fourteenth Amendment and the Slaughterhouse Cases, there is a citizen of the United States, and a citizen of a State who is not a citizen of the United States.
A citizen of the United States is recognized in Section 1, Clause 1 of the Fourteenth Amendment. A citizen of a State who is not a citizen of the United States is recognized at Article IV, Section 2, Clause 1 of the Constitution of the United States of America.
Privileges and immunities of a citizen of the United States are not the same as privileges and immunities of a citizen of a State.
A citizen of the United States can become also a citizen of a State, under Section 1, Clause 1 of the Fourteenth Amendment. Thus, a citizen of the United States would be also a citizen of a State, and would have privileges and immunities of a citizen of the United States AND privileges and immunities of a citizen of a State.
Therefore, in any State of the Union, there are two State citizens, a citizen of a State, under Article IV, Section 2, Clause 1 of the Constitution, and also a citizen of a State (and a citizen of the United States), under Section 1, Clause 1 of the Fourteenth Amendment.
A citizen of a State, since the adoption of the Fourteenth Amendment and the Slaughterhouse Cases, can be a litigant in federal court. A citizen of a State, since the adoption of the Fourteenth Amendment and the Slaughterhouse Cases, can pursue a cause of action against another citizen of a different State. A citizen of a State, since the adoption of the Fourteenth Amendment and the Slaughterhouse Cases, can be pursued in a cause of action against a citizen of a foreign State.
Legal authority quoted, cited and linked.