Arda is the name of Tolkien’s fictional world, while Middle-earth is only one of its major regions.
In Tolkien’s cosmology, Arda is the Earth, or world, created within the broader universe of Eä. It includes Middle-earth and Aman, the realm to the west where Valinor is located. During the early ages, Arda is changed by vast wars and disasters, including the destruction of Beleriand and the alteration of the world after the downfall of Númenor.
The distinction matters because Middle-earth is often used casually to mean the entire setting of Tolkien’s stories. More precisely, it is a continent or central landmass within Arda. Aman is another major part of the world, while Númenor is an island kingdom that later sinks beneath the sea.
Tolkien’s fictional geography also changes over time. The world begins as flat in the mythology and is made round after Númenor’s destruction, while Aman is removed from the ordinary physical world.