Arda is the fictional world that contains Beleriand and Númenor in J.R.R. Tolkien’s writings. It is the world created within Tolkien’s broader mythological framework.
Middle-earth is only one major region of Arda, not the name of the entire world. Aman, including Valinor, lies to the west, while Númenor was an island kingdom that existed during the Second Age before its destruction.
Beleriand was a western region of Middle-earth during the First Age. It was largely destroyed and reshaped at the end of that age. Because readers most often encounter Middle-earth, the larger name Arda is sometimes mistakenly treated as a synonym for it.