The objective of this article is to generate a discussion about how to differentiate research universities, teaching universities that do research and teaching universities. The distinction made by university taxonomies, global higher education rankings and the academic information generated by the system’s own actors is analyzed. The study demonstrates how currently taxonomies and traditional models do not characterize university systems, even in the country where they were born. The global rankings of universities prove to be a useful source of information and a way to contribute to institutional visibility and reputation. Academic information, when it comes to qualitative indicators of scientific production, finds access limitations, especially for teaching universities that carry out research. Examples of lack of methodological rigor are documented when these indicators are reused. The characterization of scientific production must balance the indicators that describe the size of the production, with those that characterize performance, impact and excellence. The analysis of the empirical information shows that some institutions, of all countries analyzed and of all sizes, have impact results that are below the world average, showing that there is no positive correlation between research performance and institutional size. The difficulty is not so much in determining when we are in front of a research university, but in defining the border between a teaching university that does research and the one that is essentially teaching. A teaching university that does research produces at least 100 articles per year, counted in five-year windows, being desirable that this size threshold be above 150 annual articles. A research university produces at least 1,000 to 2,000 articles per year and graduates at least 20 doctors per year. In both cases, the institutions must reach performance, impact and excellence indicators, both led, that demonstrate that the university has a faculty staff able to do original research autonomously, with a level of results equivalent to those of their colleagues in the world.