In conceptual modelling, there are many competing views of the role of the modelling language. In this paper, we propose a clarifying classification of different kinds of languages. This classification, based on the semantical background theory of each kind of language, divides the modelling languages into three categories: extensional modelling languages, languages based on concept calculus
... [Show full abstract] (intensional languages) and hybrid languages. The classification provides the background for studies of applicability of a modelling language. Based on an example, we observe that some features of the intensional approach are actually only terminologically different from those of the extensional one. We observe, too, that because of the clear semantic background, hybrid languages seem promising. Using them in conceptual modelling would benefit from a good methodology.