Interest. Derives from the traditional means of paying interest on a definitive, security-printed bearer bond, wherein each interest payment was represented by a detachable perforated strip on the side of the bond - you know, like coupons in the newspaper - which the bondholder would tear off and present to the paying agent in return for the interest payment in question.
Coupon can refer to any interest payment, under loans, swaps etc, or specifically to the interest payment obligation under a bond as a discrete financial instrument from its host bond. Each coupon, once detached, is its own transferable promissory note , it can trade in the same way as the bond from which it was detached trades. This is called coupon stripping.
