If Jordan annexed areas of western Palestine, that means there must have been an eastern Palestine - on the other side of the Jordan River.
The term "West Bank" didn't exist yet, so AP called it the historically accurate "western Palestine."
1950 was less than three decades removed from the original partition of Palestine into western Palestine and Transjordan, so the terms "eastern" and "western" Palestine were still used. In the 1911 Encyclopedia Britannica, the phrases "Eastern Palestine" and "Western Palestine" were capitalized.
Somehow since then the world has forgotten about eastern Palestine, mostly due to Jordan's insistence that it is not Palestine - it is so insecure that its king still insists, even today, that nations assure it that they will not consider Jordan as a Palestinian state.