We present a new study of the spatial distribution and ages of the star clusters in the Small Magellanic Cloud (SMC). To detect and estimate the ages of the star clusters we rely on the new fully automated method developed by Bitsakis+ (2017, J/ApJ/845/56). Our code detects 1319 star clusters in the central 18deg^2^ of the SMC we surveyed (1108 of which have never been reported before). The age distribution of those clusters suggests enhanced cluster formation around 240Myr ago. It also implies significant differences in the cluster distribution of the bar with respect to the rest of the galaxy, with the younger clusters being predominantly located in the bar. Having used the same setup, and data from the same surveys as for our previous study of the LMC, we are able to robustly compare the cluster properties between the two galaxies. Our results suggest that the bulk of the clusters in both galaxies were formed approximately 300Myr ago, probably during a direct collision between the two galaxies. On the other hand, the locations of the young (<=50Myr) clusters in both Magellanic Clouds, found where their bars join the HI arms, suggest that cluster formation in those regions is a result of internal dynamical processes. Finally, we discuss the potential causes of the apparent outside-in quenching of cluster formation that we observe in the SMC. Our findings are consistent with an evolutionary scheme where the interactions between the Magellanic Clouds constitute the major mechanism driving their overall evolution.