The following graph in my textbook plots the relationship of external driving frequency and phase difference of the driver and a system. From this question (Why dosn't amplitude increase when drive frequency is above resonance?) I understand that the amplitude is maximum at the natural frequency because the system and driving force are in phase. Therefore phase difference is $0$ at $f_0$. Why does this change for when damping comes into the picture. In other words, why isnt $0=f_0$ for higher damping?
I understand that the amplitude is maximum at the natural frequency because the system and driving force are in phase.
That statement is wrong.
Undamped systems a special case, and are different from damped systems because there is no work required to maintain a constant amplitude over time.
For a damped system, the maximum amplitude occurs when the driving force can do the maximum work on the system, and that is when the phase difference between force and displacements is 90 degrees. If the force was in phase with the displacement, the force would do positive work as the force and displacement both increase, but then do equal and opposite negative work as the displacement returned to zero, so the net work over a whole cycle would be zero.
In fact the general solution for an undamped system excited at is resonant frequency also has the displacement out of phase with the force, and the displacement amplitude increases linearly over time (i.e. the displacement is something like $x = x_0 t \sin \omega t$). To maintain a constant amplitude at the resonant frequency, the applied force must be zero, and therefore "the phase angle between the force and displacement" is undefined.
For any other excitation frequency, the force and displacement in an undamped system are exactly in phase below the natural frequency and out of phase (phase angle $\pi$) above it.