Today, when anyone talks about "Palestinians", we normally understand this as referring to Arabs who live in the West Bank or in Gaza, but this understanding is relatively recent. Before the 1960's, "Palestine" was a geographical region and "Palestinians" were its inhabitants, regardless of whether they were Jews or Arabs. The term "Palestinian Jew" might seem strange today, even an oxymoron, but at one time, it would have been regarded as being completely ordinary.
Some Palestinian Arabs today claim to be descended from the ancient Canaanites or the biblical Philistines, while also denying any such ancient connection for the Israeli Jews, whom they regard as modern-day invaders. The claim of Philistine descent would thus be ironic, since the historical Philistines were not indigenous to the region, but refugees from Crete and other parts of Greece, and thus invaders. Even so, the name "Palestine" was derived from the name "Philistine", bestowed by the Romans after they put down a Jewish revolt. More recently, the name "Palestine" often referred to Jews and their institutions, while Arabs in the region considered the area to be the southern part of Syria.
Read more on this subject at Myths and Facts and Arutz Sheva. Both links were found at The Religion Of Peace.