Damascus was the home city of Saladin. When he took Jerusalem, he controlled everything between Aleppo and Aqaba. Technically, his brother was to be Emir of al Kuds and King of Jerusalem, but he controlled his brother. It was not to be. The Ismailis swept down from the mountains and took Homs and Hamah when Saladin was assassinated. What could have been a great power between Egypt and Baghdad was gone in an instant, riven into city states, none of which were powerful enough to dominate the others.
Damascus is a huge, rich city on the Nahr Barada river, which empties into the desert in s series of marshes and intermittent lakes. Damascus has long been known for its legendary swordsmiths, and the best swords still come from here. The Emirs of Damascus control a large area on the verge of the desert, and Damascus is an important focus of the caravan trade across the desert and into Acre. The Emirs are generally friendly with Acre, and hostile to the Emirs of Homs and el Kuds - AKA the Kings of Jerusalem.
Galilee was a mostly Christian Principality around the lake of Galilee and Jordan River, part of the kingdom of Jerusalem, theoretically stretching from St Mamas in the north to Gadara in the south. The princes of Galilee were powerful lords in their own right, though they didn't have the freedom of action of the Counts of Tripoli or the Princes of Edessa and Antioch. Tancred, Prince of Galilee in 1425, broke his vows of fealty to the new King of Jerusalem, calling him a parricide and thus cursed by both faiths. This was, apparently true, but no king likes their faults pointed out so blatantly.
This led to war, the King of Jerusalem against the Prince of Galilee. The war was bitter and bloody, but only resolved when the Emir of Damascus came to the aid of the Prince, and together they defeated the King of Jerusalem near Belvoir in the Jordan Valley. The Prince tendered his fealty to the Emir of Damascus, and was granted much freedom of action in return.
The kings of Jerusalem have never stopped claiming Galilee, and periodically warfare flares between Galilee and Jerusalem. The borders tend to be fluid, depending on the strength of the parties concerned.
The Emirate of Damascus, and the Principality of Galilee: