There are multiple ways in which to select post-starburst galaxies in the literature. In this work, we present a study into how two well-used selection techniques have consequences on observable post-starburst galaxy parameters, such as colour, morphology and environment and how this affects interpretations of their role in the galaxy duty cycle. We identify a master sample of H$\delta$ strong (EW$_{H\delta}$ > 3\AA) post-starburst galaxies from the value-added catalogue in the 7th data release of the Sloan Digital Sky Survey (SDSS DR7) over a redshift range 0.01 -2.5$\AA) but one having an additional cut on EW$_{H\alpha}$ ($> -3$\AA). We examine the differences in observables and AGN fractions to see what effect the H$\alpha$ cut has on the properties of post-starburst galaxies and what these differing samples can tell us about the duty cycle of post-starburst galaxies. We find that H$\delta$ strong galaxies peak in the `blue cloud', E+As in the `green valley' and pure E+As in the `red sequence'. We also find that pure E+As have a more early-type morphology and a higher fraction in denser environments compared with the H$\delta$ strong and E+A galaxies. These results suggest that there is an evolutionary sequence in the post-starburst phase from blue disky galaxies with residual star formation to passive red early-types.