'Desert' in the Bible

Then the Ziphites came up to Saul to Gibeah, saying, "Doesn't David hide himself with us in the strongholds in the wood, in the hill of Hachilah, which is on the south of the desert?

They arose, and went to Ziph before Saul: but David and his men were in the wilderness of Maon, in the Arabah on the south of the desert.

The Ziphites came to Saul to Gibeah, saying, "Doesn't David hide himself in the hill of Hachilah, which is before the desert?"

Saul encamped in the hill of Hachilah, which is before the desert, by the way. But David stayed in the wilderness, and he saw that Saul came after him into the wilderness.