Arda is the name of J.R.R. Tolkien’s invented world in which Middle-earth is located.
In Tolkien’s mythology, Arda is the world or realm created within Eä, the wider universe. Middle-earth is not the entire world; it is one major region of Arda, especially central to the histories told in The Hobbit and The Lord of the Rings.
Other important regions of Arda include Aman, the western land associated with the Valar and the Elves, and Beleriand, a First Age region later destroyed or reshaped during the War of Wrath. Valinor is a part of Aman, so it is not a synonym for Arda.
The name Arda comes from Tolkien’s invented languages and is associated with the world as shaped by the events of his legendarium. Modern maps of Middle-earth therefore show only part of the larger setting.