Historically, the United States has operated under two constitutions: the Articles of Confederation from 1781 until 1788 and the Constitution from 1788 until this day. Both documents were written at the same period and by the same people, and yet, they show more differences than similarities. In fact, comparing the Articles and the Constitution is compelling because it allows one to capture what framers found important in 1781 and how their views had changed by 1788.
The Articles of Confederation state that the formal name of the nation is the United States of America while the Constitution does not specify this detail, though referring to the country in the exact same way in the Preamble (Tushnet, Graber, and Levinson 2015). In terms of legislature, the Articles saw it as unicameral, called Congress, while the Constitution made Congress bicameral, dividing it into the House of Representatives and the Senate. While the first document allowed between two and seven members per state to join Congress, the later document limited the number to two Senators per state. In turn, the number of Representatives would be apportioned based on how populous each state is.
As for the executive branch, the Articles did not provide any information while the Constitution is clear that it is represented by the President. The documents also take different stances on the national judiciary: it is the maritime judiciary as per the Articles and the Federal judiciary as per the Constitution that also includes the Supreme Court. It is the Supreme Court that was given the power to adjudicate disputes between states while earlier, this role was assigned to Congress. In essence, the Constitution addressed the weaknesses of the Articles and protected the freedom and independence of the American people.
Reference
Tushnet, Mark V., Graber, Mark A., Levinson, Sanford. 2015. The Oxford Handbook of the U.S. Constitution. Oxford: Oxford University Press.