I don't think everyone agrees, but I think usually, a closure refers to the implementation of that concept, and not the concept itself. The implementation being a pair of the static code alongside the captured environment.
Also, I think most would agree that if the "higher scope" is the global scope, then it isn't actually a closure. For example, C functions can access globals, but C has no closures (barring various extensions).
Also, I think most would agree that if the "higher scope" is the global scope, then it isn't actually a closure. For example, C functions can access globals, but C has no closures (barring various extensions).