Gandalf the White is the wizard who returns after battling the Balrog in Peter Jackson’s The Two Towers.
At the end of The Fellowship of the Ring, Gandalf falls with the Balrog of Moria after defeating the creature on the Bridge of Khazad-dûm. In The Two Towers, Aragorn, Legolas and Gimli encounter him in Fangorn Forest and initially mistake him for Saruman because of his white robes.
The film presents Gandalf’s return as a transformation. He explains that he was sent back to complete his task, and he now holds the rank previously associated with Saruman. His arrival changes the military and political situation before the Battle of Helm’s Deep.
The answer is not simply Gandalf the Grey, his earlier identity. Saruman the White is a different wizard, while Radagast the Brown belongs to the same order but does not return from Moria.