I think you are referencing the call/cc syntax and the cps programming style? Those are just different applications of the same principle. You have 'a thing' that you pass a function of 'a -> void' (or 'a -> unit') and whenever it has a value for a it will call that function.

In cps (and properly with call/cc?) you always call the given function exactly once as your function produces one value (the return value from a imperative perceptive). But there is no rule that says that you can't call the given function multiple times (or even never). You will (practically) never do it with cps because that is not how cps is supposed to work, but that is just one of the many applications of continuations.

Continuations can also be used to abstract the imperative style event listeners JavaScript is riddled with. They are also 'a thing' that you give a function 'a -> void' that will call that function whenever they have a value for a. There are ones that only call the function once (for example an onDomLoaded listener), but there are also ones that call it many times as they generate multiple a's over time (for example an onKeyboardPressed listener). You properly wont see this in very functional languages as those already hide the outside world for you behind a very pure interface.

Those are just all the same abstraction of 'a thing' that eventually calls a function 'a -> void'. Continuations are an extremely abstract concept and cps is just one practical application of them. If you see continuations as just the things you can do with your call/cc syntax then you are missing out on a lot of the things they are capable of and how powerful of an idea they really are.