Ontic structural realism (hereafter OSR) is one of the most significant ontological attitudes toward modern physics. On close examination, OSR can be classified into several versions in terms of the relative ontological status of objects and relations. Previous studies have not carefully dealt with the differences among the several versions of OSR, mainly because the meanings of some metaphysical concepts are ambiguous. Among them, one way to formulate OSR is to appeal to the idea of identity. However, “identity” can be regarded as either numerical identity or essence. In this article, the derivations of OSR’s minimal statements from the cases in quantum theory give a clear-cut explanation about relationships between metaphysical and scientific statements and show that the formulation of OSR should be based on essence.