Exact definition of overshoot
When you mention an example where steady state is unity, that is normalized. Typically we are only interested in the percent overshoot, so unity makes it easy to scale. I.e. If a system has 10% overshoot on a system that's steady state is unity, the max peak is 1.10. 

Your definition is identical to the control systems approach. Overshoot is simply the difference between the max peak and the steady state value. If a system has a quick response, it will typically have a larger overshoot value. If a system has a slow response, typically the overshoot is very small.

This image has a good breakdown of a response. You can see that the overshoot is simply the difference between the max and steady state value.



Hope this helps. If you have any other questions, please shoot them my way. 

Good luck! - Josh

EDIT

This is a page out of the book I use: