A rhizome is a horizontal, usually underground stem of a plant that often sends out roots and shoots from its nodes. They are also referred to as creeping rootstalks, or rootstocks. A stolon is similar to a rhizome, but exists above ground, sprouting from an existing stem.
A tuber is a thickened part of a rhizome that has been enlarged for use as a storage organ. They are typically high in starch.