Here "righteousness" means being right with God. Alternate translation: "being right with God through trusting Jesus Christ" (See: [[rc://en/ta/man/jit/figs-explicit]])
Paul implies that God accepts all people in the same way. Alternate translation: "There is no difference at all between the Jews and the Gentiles" (See: [[rc://en/ta/man/jit/figs-explicit]])