Motion-position illusions (MPIs) are visual motion illusions in which motion signals bias the perceived position of an object. Due to phenomenological similarities between these illusions, previous research has assumed that some are caused by common mechanisms. However, this assumption has yet to be directly tested. This study investigates this assumption by exploiting between-participant variations in illusion magnitude. During two sessions, 106 participants viewed the flash-lag effect, luminance flash-lag effect, Fröhlich effect, flash-drag effect, flash-grab effect, motion-induced position shift, twinkle-goes effect, and the flash-jump effect. For each effect, the magnitude of the illusion was reliable within participants, strongly correlating between sessions. When the pairwise correlations of averaged illusions magnitudes were explored, two clusters of statistically significant positively correlated illusions were identified. The first cluster comprised the flash-grab effect, motion-induced position shift, and twinkle-goes effect. The second cluster comprised the Fröhlich and flash-drag effect. The fact that within each of these two clusters, individual differences in illusion magnitude were correlated suggests that these clusters may reflect shared underlying mechanisms. An exploratory factor analysis provided additional evidence that these correlated clusters shared an underlying factor, with each cluster loading onto their own factor. Overall, our results reveal that, contrary to the prevailing perspective in the literature, while some motion-position illusions share processes, most of these illusions are unlikely to reflect any shared processes, instead implicating unique mechanisms.