Two separate `schools' have offered what are claimed to be general foundations for the subject of non-equilibrium statistical mechanics, based respectively on subdynamics and information theory. These appear to be unrelated, to start from conflicting interpretations of probability, to generate different methodology and to be useful in non-overlapping applications. The present paper is a study of the relation between the work of the two schools. After reviewing them critically in a presentation that unifies the notation used, the connection between them is developed. It is concluded, subject to some provisos, that they are equivalent. It is suggested that the subject could be unified on this basis, and that the methodologies be made more generally available.