The terms "Arians", "Messalians", and "Manicheans" were widely used in Christian medieval anti-heretical writing to describe contemporary dissidents. These terms were often part of wider typologies and genealogies. To a varying degree, medieval terms and ideas about continuity and the origins of heterodox groups have influenced modern research. Mainly, alleged analogies between catharism and bogomilism, on the one hand, and manicheism, on the other, and genealogical narrations about the Manichean origins of some medieval heterodox movements have been recycled by modern historians. The polemical origin of these ideas does not, in itself, necessarily mean that they are irrelevant or unscientific. However, the paper argues that there are some rules to be observed while creating or taking over any term, typology, or genealogy. It also argues that the terms and typological or genealogical ideas presented here do not observe such rules. The paper points to three basic rules: (1) terms, methods, and theories used must not be influenced by aims whose compatibility with the aims of science cannot be shown; (2) scientific terms, typologies, and genealogies have to be based on a transparent and consistent argument; (3) any piece of knowledge has to be relatable to the used theories and methods.