What was Thomas Jefferson saying the peaceful transition from one government (Federalist Party) to another (Republican Party) ?

Amidst threats of violence and fears of national dissolution, Congress met in February 1801 to resolve the fiercely contested election of 1800. Federalists and Republicans argued over how best to implement the new federal Constitution, but both parties accepted the Constitution as the framework in which to settle the dispute. With Aaron Burr and Thomas Jefferson tied, the decision rested with the House of Representatives. The political parties, which had just brought the nation to the verge of disaster, now served as the instruments to mediate a political solution that ultimately elected Jefferson as president. In his inaugural address Jefferson sought to alleviate national fears by making his now-famous unifying declaration: "We are all republicans. We are all federalists."

"But every difference of opinion is not a difference of principle. We have called by different names brethren of the same principle. We are all republicans. We are all federalists."

Thomas Jefferson First Inaugural Address, March 4, 1801