Imposing integrity constraints is an efficient way to improve data quality in databases. Effective imposition of integrity constraints requires their precise distinction and specification. Despite a few efforts for enhancing the distinction and specification of the integrity constraints in spatial and spatiotemporal databases by their classifications, these classifications fail to precisely distinguish between inherently dissimilar integrity constraints. Furthermore, the existing classifications provide imprecise definitions for the classes of integrity constraints. Such shortcomings explain why still diverse terms are used to refer to a same spatial integrity constraint. In this paper, we propose a formal and more exhaustive classification of the integrity constraints in spatiotemporal databases relying on their nature with respect to space, time, and themes. Moreover, a terminology for the integrity constraints of spatiotemporal databases is presented. Finally, we discuss the advantages of the proposed classification in the specification of integrity constraints.