A Steiner triple system of order n is a collection of subsets of size three, taken from the n-element set {0, 1, ..., n-1}, such that every pair is contained in exactly one of the subsets. The subsets are called triples, and a block-intersection graph is constructed by having each triple correspond to a vertex. If two triples have a non-empty intersection, an edge is inserted between their vertices. It is known that there are eighty Steiner triple systems of order 15 up to isomorphism. In this paper, we attempt to distinguish the eighty systems using their block-intersection graphs, as well as discuss general properties of block-intersection graphs of Steiner triple systems.