No ... it’s pretty much this way ... Hamas in Gaza, the Palestinian Authority in Judea and Samaria (i.e., the Westbank). The P.A. and Hamas are deadly enemies; they kill each other. Hamas gained control over Gaza a while back and kicked the PA out of there.
Even Egypt recognizes that the PA and Hamas are different. Egypt wants Abbas and the PA to control the Gaza/Egypt border and NOT Hamas. Hamas and the Muslim Brotherhood have worked together, and Egypt wants nothing to do with either of them.
In the beginning when Hamas was first formed, Israel actually supported Hamas (under the surface) in order to provide an offset to Arafat and the PLO (the forerunner to the PA).
Thanks for the clarification.