The word key is both an adjective and a noun meaning something is important. But which is the preferred one to use in terms of different territories? For example, should I say
The hint is key.
The hint is the key.
In the first sentence, key means critical, crucial. And in the second sentence, key means the deciding factor for solving a problem.
As an English learner, I'm more interested in AmE and BrE, while usages in other places are also helpful to me. So which one sounds better to the those native speakers? Or are they interchangeable if they both mean something crucially important?