I thought Moshe Dayan gave it to the waqf after it was liberated by the IDF in 1967
shalom b'SHEM Yah'shua HaMashiach Dayan combined a kibbutznik's secular identity and pragmatism with a deep love and appreciation for the Jewish people and the land of Israel --but not a religious identification. In one recollection, having seen rabbis flocking on the Temple Mount shortly after Jerusalem was captured in 1967, he asked "what is this? Vatican?" Dayan later ordered the Israeli flag removed from the Dome of the Rock, and gave administrative control of the Temple Mount over to the Waqf, a Muslim council. Dayan believed that the Temple Mount was more important to Judaism as a historical rather than holy site.
It’s a distinction without a difference, IMHO.
I use them all interchangeably.
Specifically, Sheik Azzam Khateeb is the new manager of the Waqf is a Jordanian monarchy stooge.
They’ve been buying up surrounding land, too.