This paper addresses a data analysis task, known as contrast set mining, whose goal is to find differences between contrasting groups. As a methodological novelty, it is shown that this task can be effectively solved by transforming it to a more common and well-understood subgroup discovery task. The transformation is studied in two learning settings, a one-versus-all and a pairwise contrast set mining setting, uncovering the conditions for each of the two choices. Moreover, the paper shows that the explanatory potential of discovered contrast sets can be improved by offering additional contrast set descriptors, called the supporting factors. The proposed methodology has been applied to uncover distinguishing characteristics of two groups of brain stroke patients, both with rapidly developing loss of brain function due to ischemia:those with ischemia caused by thrombosis and by embolism, respectively.