Feigned fleeing or farciful forestalling?

[alatar]

Originally Posted by Gandalf, during the Council of Elrond

Yet at last, as his shadow grew, Saruman yielded, and the Council put forth its strength and drove the evil out of Mirkwood - and that was the very year of the finding of this Ring: a strange chance, if chance it was.

But we were too late, as Elrond foresaw. Sauron also had watched us, and had long prepared against our stroke, governing Mordor from afar through Minas Morgul, where his Nine servants dwelt, until all was ready. Then he gave way before us, but only feigned to flee, and soon after came to the Dark Tower and openly declared himself.

Originally Posted by Gandalf, a little later in the monologue

But Saruman has long studied the arts of the Enemy himself, and thus we have often been able to forestall him. It was by the devices of Saruman that we drove him from Dol Guldur. It might be that he had found some weapons that would drive back the Nine.

The two quotes above, from The Fellowship of the Ring, show Gandalf presenting two different versions of what befell Sauron at Dol Guldur. In the first, the White Council makes to drive him out, but Sauron leaves of his own volition. Dol Guldur was just a temporary residence while Mordor was being made ready - and it was close to the Gladden Fields as well. In Gandalf's second comment, we have Saruman credited with some super weapon or stratagem that drives Sauron from Dol Guldur.

So which is it? Was Sauron flying or faking?