Jamieson, Fausset and Brown on 1 Samuel 27:2-3

2-3. Achish, the son of Maoch, king of Gath--The popular description of this king's family creates a presumption that he was a different king from the reigning sovereign on David's first visit to Gath. Whether David had received a special invitation from him or a mere permission to enter his territories, cannot be determined. It is probable that the former was the case. From the universal notoriety given to the feud between Saul and David, which had now become irreconcilable, it might appear to Achish good policy to harbor him as a guest, and so the better pave the way for the hostile measures against Israel which the Philistines were at this time meditating.

1Sa 27:5-12. David Begs Ziklag of Achish.