The Israeli region is called Palestine because the Roman Emperor Hadrian gave it that name in 135 A.D. after the second Jewish revolt. It was propaganda to name the land after Israel's enemies, the Philistines.
Before the modern state of Israel was formed in 1948, "Palestinian" referred to Jews in the region. Many of the Arabs were recent immigrants who came to participate in the thriving Zionist economy.
In 1950, Jordan annexed the West Bank, so they annexed responsibility for their Arab brothers living there. The Palestinian Arabs in Judea and Samaria -- no matter where they originated -- became Jordanians in 1950. Jordan itself did not exist until after WW1, and Jordanians are not ethnically distinct. In ethnic and cultural terms, the "Palestinian" Arabs are equally Jordanian.
Interesting read: Debunking the claim that "Palestinians" are the indigenous people of Israel