In this paper we are concerned with the degree to which modeling languages explicitly accommodate conceptual distinctions. Such distinctions refer to the precision and nuance with which a given modeling concept in a language can be interpreted (e.g., can an actor be a human, an abstraction, or a collection of things). We start by elaborating on the notion of conceptual distinctions, while also providing a list of common modeling concepts and related distinctions that are relevant to enterprise modeling. Based on this, we will then analyze a number of conceptual modeling languages to see whether they accommodate the explicit modeling of (potentially important) conceptual distinctions - that is, whether they have specific language elements to model conceptually distinct entities with. On basis of these findings we then further discuss how to ensure such different distinctions are captured in created models, how to know which of them to support in modeling languages, and where existing methods fall short. We conclude by discussing what impact our findings may have on the use (and validation) of modeling languages.