Rhizome or Bulb?
True bulbs are comprised of two distinct types, tunicate and imbricate bulbs.
Their tough paper like tunic distinguishes the tunicate bulbs, and this covering protects them from drying out, and thus the bulbs can be stored in a cool dry place for several months. From the bulb basal plate, from which the roots develop, there are concentric fleshy scales that surround the short stem and bud that arises from the base through the center of the bulb. The onion, daffodil, hyacinth, tulip, amaryllis, and other bulbs with a tunic or paper like covering, are well known examples. Iris growers are familiar with iris reticulata, iris danfordiae, and the Dutch and English irises, which are also tunicate bulbs.
Imbricate bulbs do not have the tunic and must be kept from drying out during the period of time that they are out of the ground before resetting into the garden. They are stored in a slightly moist medium during storage and shipment. Like the tunicate bulbs the roots develop from the basal plate, while the fleshy scales where the nutrients are stored are overlapped around the circumference of the bulb with the stem-bud rising through the center of the bulb, which is composed of these overlapping fleshy imbricate scales. The bulbs of the lily family are prime examples.
Corms are often lumped together, in the minds of some people, with tunicate and imbricate bulbs and referred to with the general term bulbs. There is quite a difference in the make up of the corm, though. The base of the corm from which the roots develop is topped with the short stem-bud, which is surrounded with a storage structure of undifferentiated substance covered with a thin brownish paper-like tunic. If you cut it in cross section you do not see the concentric rings or imbricate scales of which the true bulbs are composed. The new corm each year is formed just above the old spent corm with a lot of little corms around its base. This results in it becoming nearer the surface of the soil each year, if they are not reset on a regular basis. Crocus and gladiolus with which every one is familiar develop from Corms.
Tubers are a third type of underground structure often referred to with the general term bulb. They differ from the true bulbs, and from the corm by not having a stem-bud base from which the roots develop. Instead they have buds, which are scattered over their surface from which the plants sprout a shoot from which the roots develop. The familiar Irish potato, which we all know very well, along with the caladium, anemones, and oxalis, are good examples of tubers.
The tuberous roots of Dahlias differ from the other tubers by having the buds confined to that area at the top of the swollen elongated root where the stem from last year is attached. A portion of this stem base must be included in any division of the tubers to provide a place from which the new plant bud and shoot can develop. In tuberous rooted begonia the new buds all develop from the top of the round flat tuber. These nutrient storage structures are significantly different from rhizomes in that they are true roots, where as the swollen elongated rhizome's storage structure is a true stem.