How to differentiate step responses of 1st-order and 2nd-order systems?

Question

How can one determine if a system is of 1^st or 2^nd order by merely looking at the step response of the system or device?

One can easily spot an underdamped response straightaway by the overshoots, but the step response of first-order and second-order critically damped and overdamped systems look very similar.

Is there a key to differentiating these responses from a graph?

Figures

First order step response

Second order step response

Answer 1

Over damped responses hit an aysmptote below the $100%$ maximum signal mark. Which is the mark that under damped systems orbit and critically damped systems go to.

Answer 2

If the curve has an inflection point, then the system is second order. Otherwise, I am afraid that there is little you can do.