> The dirty little secret in CS is that unit, functional, and end-to-end tests are all the exact same thing.
I agree that the boundaries may be blurred in practice, but I still think that there is distinction.
> visible, public interface
Visible to whom? A class can have public methods available to other classes, a module can have public members available to other modules, a service can have public API that other services can call through network etc
I think that the difference is the level of abstraction we operate on:
unit -> functional -> integration -> e2e
Unit is the lowest level of abstraction and e2e is the highest.