A corm is a solid tissue mass with specific points for growth nodes and roots, such as gladiolus, crocus.
A tuber is and underground stem capable of producing buds and roots, such as begonia or calla.
A rhizome is a swollen root modified to be come a storage organ and capable of the same, eremurus, lily of the valley,aconitum.
They are in general called "bulbs". They are underground storage organs developed to overcome adverse climate conditions
and capable of producing above ground plants at certain times and survive mostly by devision.
If you familiarize yourself with the origin and natural growing conditions of these plants, you can avoid a great many costly mistakes. For instance, a plant that originates from a harsh land-climate will not do well in a tropical or sub-tropical climate, although it might prosper on higher elevations in such a climate.