Band Aid vs adhesive bandage

Band Aid and adhesive bandage both are nouns.

Word	Noun	Adjective	Verb	Adverb
Band Aid	Yes	No	No	No
adhesive bandage	Yes	No	No	No

As nouns, adhesive bandage is a hypernym of Band Aid; that is, adhesive bandage is a word with a broader meaning than Band Aid:

Band Aid: trade name for an adhesive bandage to cover small cuts or blisters
adhesive bandage: bandage consisting of a medical dressing of plain absorbent gauze held in place by a plastic or fabric tape coated with adhesive

Band Aid (noun)	adhesive bandage (noun)
trade name for an adhesive bandage to cover small cuts or blisters	bandage consisting of a medical dressing of plain absorbent gauze held in place by a plastic or fabric tape coated with adhesive