I failed to equate them as the same hill probably from experience.

The Temple Mount is assumed to be on Mt. Moriah, and Holy Sepulchre Church across town boasts a "Golgotha" -- a narrow set of stairs to an upper church, adorned with a gorgeous icon of the Crucifixion attended by the mother of Jesus and the beloved disciple, and an altar under which it is customary to kneel for a brief time (Rev. 6:9) and to peer through a split in the marble floor, evidence of an earthquake. And light a taper, of course.

I won't argue with you that they are the same hill -- that is fitting -- but from a practical standpoint, it is unlikely that a Christian church commemorating the death and burial of Jesus Christ would be permitted to stand on the actual site, upon the Temple Mount, so Christians make due across town and, for that reason, in my mind at least, the hills are separate.