The properties of transfer functions are best described and characterized by the locations of the poles and zeroes in the frequency domain. This applies primarily for filter applications. In control systems, very often we make also use from the characteristics in the time domain (step response).
For a 1st-order system, there is only one real pole which - in the time domain - corresponds to an exponential step response. Only for such a function we can define a single time constant which describes how fast the step response is approaching its final value.
For 2nd-order systems, there are several different transfer functions which allow to define two different factors (dimension: time). Such an interpretation in the time domain (step response) is important, in particular, for control systems (and less important for filters, for example). These factors (time constants) describe (a) the form and (b) the time which is needed to reach the final state of the step response.
Examples (controllers): P-T2, D-T2, I-T1, PD-T1, PI, PID,....
Selected example (PD-T1): H(s)=K(1+sT2)/(1+sT1).... with T2>T1.
Step response: The asymptote at t=0 crosses the time axis at t=T1. The value at t=0 is g(t=0)=K*T2/T1.