There are many plants that present themselves as bulbs or bulbous plants. As such the terms are often confusing. This brief summary helps to explain the differences of these bulbous structures.
 
Modified Roots
Fleshy Storage – The root organ is fleshy.
Example: carrot (Daucus carota).
Tuber Storage – The root is swollen as a tuber.
Examples: sweet potato, asparagus, cassava (Manihot esculenta).
 
Modified Stems
Rhizome – Most rhizomes bear adventitious roots. Rhizomes are usually covered with scale leaves in the axils of which are axillary buds. Like all stems, rhizomes have nodes and internodes. Example: Shot Eye (Canna), Daylilies (Hemerocallis) and Mother-in-law Tongue (Sanserveria).

Stem Tuber – These are solid thickened stems or branches serving as storage organs and providing opportunity for vegetative propagation. They may be formed on rhizomes, axillary branches or main stems, either above or below the ground. Example: Potato (Solanum tuberosum) which is a branched tuber; Nutgrass (Cyperus rotundus) which is from a branched rhizome.

Corm – Underground contracted swollen main stem in which the principal axis is vertical. On top of the corm is an apical bud which produces shoots with flowers the following season. It also produces adventitious roots. A corm is usually covered with fibrous remains of leaf bases of the previous year. The original corm loses its supply of food to support the growth of new shoots in summer then it shrivels to allow new corms to be formed. Example: Gladiolus.

Modified Leaves
Bulb – A short axis surrounded by thick fleshy leaves or leaf bases filled with food reserves. Axillary buds are to be found between the fleshy leaves and the stem bears adventitious roots. Example: onion, narcissus, tulips.

Bulbil – Axillary buds on aerial shoots transformed into ‘bulbs’ readily detach and from effective agents of vegetative reproduction. Example: Lilium bulbiferum. Note: some plants also develop bulbils from the flowers (example: Agave, Allium).

Storage (other than bulbs and bulbils) – some plants like Oxalis from fleshy storage leaf bases in clusters at intervals on rhizomes.