little wilson (paraphrased)
Brandon confirmed that "the element" is the bead of lerasium. Which confirms both this theory, and the theory that Hoid wrote the letter.
When I asked the question, I also thought the element and the lerasium were different. I asked it as a "Hoid clearly has a habit for taking important items. He has the bead of lerasium and the element. What other items does he have that we should know about?"
Brandon Sanderson (paraphrased)
Brandon's response was that the bead and the element are the same. And that he has many items he should not have.