The term local church in its theological sense refers to the diocese, with the bishop presiding at the Eucharist, surrounded by his clergy, with the laity gathered together with him. That all local churches are thus absolutely equal in this theological, Eucharistic sense, is an axiom of ecclesiology.
In recent centuries, with the advent of national autocephalous churches—collections of dioceses aggregated under a primate whose boundaries coincide with a sovereign secular state—some of the Slavic churches have begun transferring the term local church to refer to these national churches. That is, it is being used to refer not to dioceses but rather to supra-diocesan structures, which are temporal and have always changed throughout history.
This difference in usage has caused controversy, particularly between these national churches and the ancient patriarchates, whose borders do not usually fall along the same lines as secular states. The controversy comes into play when the theological truth of the equality of dioceses comes to be transferred to create an equality of supra-diocesan structures, that is, that all autocephalous churches are to be considered equal.