No, they are quite different. If you could see the side profile of the nipple button you would have eliminated that thought right away. Plus the metal is wrong, as is the iron on the back of the unknown. That said it does look old but not sure what type of button, if it even is a button. I have seen brass ones with a nipple, but they have no iron content.
He found one that looks very similar (5th picture down). It doesn't show the back of it, but he says it is a "Nipple-type leather mount and dress button. They should date from the 17th Century".