In C++, int f(void) is indeed a deprecated declaration which is 100% equivalent to int f(). It is the same signature. The void in this context is as significant as e.g. whitespace. That also means that they are subject to the One Definition Rule (they don't overload) and Derived::f(void) overrides Base::f().
Don't mess with stuff like f(const void), though. There's not a lot of consensus what that kind of weirdness means.