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ויהי מבדיל בין מים למים
And YHWH said unto Moses, Go down, charge the people, lest they break through unto YHWH to gaze, and many of them perish.
And let the priests also, which come near to YHWH, sanctify themselves, lest YHWH break forth upon them.
And Moses said unto YHWH, The people cannot come up to mount Sinai: for thou chargedst us, saying, Set bounds about the mount, and sanctify it.
And YHWH said unto him, Away, get thee down, and thou shalt come up, thou, and Aaron with thee: but let not the priests and the people break through to come up unto YHWH, lest he break forth upon them.
So Moses went down unto the people, and spake unto them.
Exodus 19:21-25
And Elohim spake all these words, saying,
I [am] YHWH thy Elah, which have brought thee out of the land of Egypt, out of the house of bondage.
Thou shalt have no other Elohim before me.
Exodus 20:1-3
1)YHVH spoke to Moses.
2) Moses listens.
3) Moses goes down and speaks to the people
4) while Moses is down, a "lower" more down to earth revelation of God, described as Elohim, delivers the famous 10 statements ( commandments ) to ALL THE PEOPLE.
Because the 10 are delivered to ALL the people it is a more down to earth revelation, thus, the name shifts.