Talk about making something complicated.
The key point here is that pitch attitude can only be used to control one parameter.
This is fundamentally true regardless of the control mechanism (raw data human pilot, manual flight following a Flight Director, or autopilot engaged)
In level change the pitch attitude is controlled to maintain a speed (IAS or Mach). Speed lower than target? Pitch down. Speed higher than target? Pitch up.
In Vertical Speed the pitch attitude is controlled to maintain a vertical speed (fpm). Vertical speed more positive than target? Pitch down. Vertical speed more negative than target? Pitch Up.
That's the fundemental difference. Everything else is type dependant.