An adhesive is a substance that sticks two things together — glue, paste, cement, the sticky layer on tape. It is the general, slightly technical word that covers all of them. On a product label or in a hardware shop you will see 'strong adhesive'; in the kitchen you would just say 'glue'.

It is also an adjective meaning 'able to stick': adhesive tape, adhesive bandage, an adhesive strip on an envelope. In fact you will meet the adjective more often than the noun, because it lives in so many product names.

On register: adhesive is the formal or trade word, glue is the everyday one. A dentist uses adhesive, a child uses glue, and both are talking about the same idea. If you are writing instructions or a report, adhesive; if you are speaking, glue.

One small thing about counting. Adhesive can be countable when you mean a type — 'they tested three adhesives' — and uncountable when you mean the stuff itself — 'apply adhesive to both surfaces'. Both are correct; the type-meaning is what makes the plural possible.

Though actually — the -ive ending here means 'having a tendency to do this', so adhesive really means 'the sticking kind of thing'. That same ending is quietly doing the same job in active, creative, and expensive, and once students see it in one word they start seeing it everywhere.