Radak: There it discusses when David struck Aram. I do not know why it was repeated. Perhaps now he says so for the future. Here he does not mention that war at all. The verses that he changed here are about the gathering of exiles. Yisrael will return to their places, just like there, they returned to their places that Melech Aram had taken.

Malbim: Also verses 2-6 are from above, 57:8-12, when he was in the cave, fleeing from Sha'ul. He was at the ultimate despair, and was saved suddenly. Also Mizmor 60 discusses when Yisrael were at the ultimate despair, and it seemed that Hashem abandoned them, and they were saved suddenly. Later, David combined the two into one Mizmor, to sing to Hashem for salvation of the individual and of the Klal, and to remember via it the miracle done for him and for His nation.