J.R.R. Tolkien’s fictional world is called Arda, while Middle-earth refers more specifically to its central inhabited lands.
Arda was created by Tolkien as the world in which the history of his legendarium unfolds. It includes the continents and regions involved in the stories of the Ainur, Elves, Men, Dwarves and other peoples. Middle-earth is therefore part of Arda rather than a complete synonym for the entire cosmic setting.
The term Arda comes from Tolkien’s invented languages and is commonly translated as “the Realm.” Its geography changes dramatically across the mythology. Major transformations include the destruction of Beleriand at the end of the First Age and the reshaping of the world after Númenor’s downfall.
Valinor is a region in Aman, the western continent, and Númenor is an island kingdom of Men. Beleriand is a First Age land west of the later Middle-earth. These names are sometimes treated as interchangeable with the whole setting, but each identifies a distinct place within Tolkien’s geography.