Take your pick. Since the Book of Deuteronomy is known to be a forgery created in the time of King Josiah, you might pick the former. Of course, since the Exodus itself never happened, you might prefer to pick the story in 3 Nephi (ch xi) where Jesus appears to a few million inhabitants of North America. Or not.
My take on all this: as the romans said, Mundus vuli decipi.
You are misreading. Exodus Chapter 20 shows Israel asking Moses to speak after they had experienced the terror of God’s voice. And then Moses begins to repeat other things that God intended the people to hear.