Overshoot percentage of a critically damped system
Simply put, the second diagram cannot exist as shown. If an LTI system overshoots at all, there must be an oscillatory component to the decay of the error waveform. Remember, the behavior of the system must be qualitatively identical, regardless of the initial value of the error!

Critically damped is when the system is on the verge of oscillatory decay. There is only one point at which this happens.

On the other hand, minimum settling time to within a certain error tolerance does allow a small amount of underdamping, with oscillation. Perhaps that's the distinction that the book is trying to make.