In the Lord of Rings The Two Towers (Extended Edition), Merry and Pippin met Saruman or Gandalf the White. I am confused. If so, what happened next?
Because what we see next is the following scene, which seems to happen some time later:
That was Gandalf, not Saruman. You're right in assuming they think it's Saruman:
We see Merry & Pippin as they flee into the forest pursued by the orc who previously attacked them. They are aided by Treebeard the oldest of the tree-like creatures, the Ents, who takes them to the one he calls the white wizard, whom Merry & Pippin assume to be Saruman; we leave them looking up at him.
but by then, Gandalf is already not 'the Gray' anymore, but Gandalf the White.
If I remember correctly, in the original books, this scene does not happen; instead, the hobbits meet Treebeard the Ent a little after they leave the Rohan vs. Orcs battlefield, and do not meet any wizards until the battle of Isengard. Another part of the Fellowship, namely Aragorn, Legolas and Gimli, do meet a white wizard in Fangorn Forest, and it's Gandalf, not Saruman.