The First Temple and the Second Temple were not the same. Not in their physical structure, and not in the quality of divine light that dwelled within them. Rabbi Schneur Zalman of Liadi explains the difference with a precision that illuminates the entire Kabbalistic understanding of sacred space.
In the First Temple, the Ark and the Tablets of the Ten Commandments rested in the Holy of Holies. The Shechinah (שכינה) that dwelled there was not the ordinary Shechinah that filters down through the standard chain of worlds. The Ten Commandments are the all-embracing principles of the entire Torah, originating in Chochmah Ila'ah (חכמה עילאה), the highest wisdom of the world of Atzilut (אצילות). To engrave these words on physical stone, the Shechinah bypassed the normal descent. "The work of God, and the writing is the writing of God" (Exodus 32:16) means these tablets were not natural. They were supernatural, a direct intrusion of the highest light into the lowest world.
The Second Temple had no Ark and no Tablets (Yoma 21b). The Talmud says the Shechinah did not abide there in the same way (Yoma 9b). The light that filled the Second Temple came through the ordinary chain of descent, step by step, world by world, until it reached the physical Holy of Holies. It was still the Shechinah. But it was Shechinah filtered through the full hierarchy of concealment.
And after the destruction of the Second Temple? "The Holy One has only the four cubits of halacha (Jewish religious law)h" (Berachot 8a). Every person studying Torah alone hosts the Shechinah. Every three who sit in judgment host it. Every ten who pray together. The Temple was a place. Torah study is a practice. The light did not disappear when the walls came down. It found new vessels.