Delay-coupled semiconductor lasers have become paradigmatic systems to study and take advantage of high-dimensional chaos. We find that the dynamic properties of delayed-feedback semiconductor lasers are determined by two main ratios of time scales: the ratio of the relaxation oscillation frequency and the feedback-induced frequency shift, and the ratio of relaxation oscillation frequency and cavity round trip frequency. Based on this insight, we demonstrate similarity properties for long delays, i.e. similar dynamics for different pump currents when adjusting the feedback strength. For different delay times, even the same time- and amplitude-rescaled version of the dynamics can be generated. We relate these findings to the mechanism for the emergence of strong chaos in delay-coupled semiconductor lasers. The presented results have major consequences for the characterization and tailoring of the dynamics for applications.