en.wikipedia.org/wiki/Adhesive_bandage

Authoritative FDA sources define medical adhesive tape and adhesive bandages as wound-care devices: strips of fabric or plastic with adhesive that are used to cover and protect wounds or hold together the skin edges of a wound and are applied to minor cuts and lacerations. By contrast, the FDA describes transdermal products as transdermal delivery systems (TDS), also known as patches, that deliver drugs through the skin into systemic circulation and are regulated as complex drug-device combination products.

So while a transdermal patch is adhesive and sticks to the skin, calling it an adhesive bandage is inaccurate. In FDA terminology, these are different product types with different intended uses: wound protection/closure vs. medication delivery through the skin.