Word
License key
A license key is a code that proves you bought something, and unlocks the copy you are running.
Also called: activation key, unlock code
A different animal from an API key, even though both are long strings you paste somewhere. An API key lets your software use a service, and usually spends money as it goes. A license key only says you paid; software you buy for your own use may check one when it starts, or when it looks for an update.
It is not a secret in quite the same way, since leaking one costs you a seat rather than your account. Treat it like one anyway and keep it out of your code. Lose it and the seller can reissue it, which is more than anyone can do for a leaked API key.