The title says David "pretended to be insane before Abimelech" (34:1). Doesn't 1 Samuel 21 say it was Achish?

Each text says what it says. 1 Samuel 21 tells how "David arose and fled that day for fear of Saul, and went to Achish the king of Gath" (1 Samuel 21:10), and "pretended to be insane in their hands" (1 Samuel 21:13); Achish said, "Look, you see the man is insane. Why then have you brought him to me?" (1 Samuel 21:14). The psalm's title reads, "By David; when he pretended to be insane before Abimelech, who drove him away, and he departed" (Psalm 34:1). In Hebrew the title's "pretended to be insane" has the words of 1 Samuel 21:13's "He changed his behavior". The title names Abimelech; 1 Samuel 21 names Achish. Neither passage explains the difference, 1 Samuel 21 doesn't mention the psalm, and these notes don't reconcile them. 1 Samuel 21's notes set the two titles that speak of David and the Philistines side by side (Psalm 34:1, 56:1).