What happened to Moses' staff?

I had presumed there was one staff through which God performed the miracles, regardless the hand that held it--and that it was the rod or staff that was placed in the Ark of the Covenant. But, silly me, after watching a secular show about Biblical relics, I deduced Aaron's budding staff wasn't the same as Moses' rod(?) I was rather confused since God turned Moses' staff into a snake in the wilderness, but turned Aaron's into a snake before Pharaoh.