In J.R.R. Tolkien’s mythology, Earth is called Arda.
Arda is the world created by Eru Ilúvatar and shaped through the events described in Tolkien’s legendarium. Middle-earth is not the entire planet; it is one major region of Arda, especially prominent in The Hobbit and The Lord of the Rings.
The history of Arda includes changing continents, divine powers, Elves, Men, and many successive ages. Its geography changes dramatically after major events, including the downfall of Númenor and the transformation of the world from a flat form into a round one in Tolkien’s later cosmological conception.
Aman and Valinor are places within Arda rather than alternative names for the whole world. Beleriand was another region, important in the First Age, that was largely destroyed during the War of Wrath.