As I've mentioned in a previous post, I think that one of the things that causes confusion among Presbyterian and Reformed churches with regard to issues of church unity and authority is the idea of "fraternal relations" between churches.
Under a presbyterian system of church government, denominational division necessarily involves a charge of schism from one denomination to the other and a rejection of the de jure legitimacy of the other denomination's officers, church courts, etc. For if there was no charge of schism, and there was a de jure recognition of authority, this would be the same as being one and not two denominations. (See here and here for earlier discussions of this basic principle.)
However, many Presbyterian churches that are out of full communion with each other nevertheless keep up the practice of maintaining "fraternal relations," or relations of "ecclesiastical fellowship," as the OPC puts it. A document expressing the OPC's position on the unity of the church titled "Biblical Principles of the Unity of the Church" describes relations of ecclesiastical fellowship as involving a situation where "official interchange may take place including the exchange of delegates at the meetings of the ruling bodies of the church," and where "[t]here will be fellowship and cooperation in organizations, both domestic
and international, which give expression to oneness of faith and life." Fundamentally, a relationship of ecclesiastical fellowship between denominations involves "[t]he recognition of each other as true churches of Christ, more or less pure (Confession of Faith XXV.4), in which the marks of the church are found."
So what exactly does this mean in light of the fact of denominational separation? Some I have spoken to have suggested that fraternal relations implies a recognition of de jure authority between denominations. But this does not seem to be the case, because, in practice, there is no such recognition of de jure authority. OPC presbyteries do not invite to their meetings, as full voting members, officers from other denominations functioning within their regions, nor do the church courts of the different denominations find any unity in any binding umbrella councils. There is thus a refusal to grant the rights and privileges which ought to be granted to de jure officers and church courts. When the roll is taken in an OPC presbytery meeting, for example, the various churches of the OPC in the region are mentioned along with their ministers and any ruling elders sent to the presbytery meeting, and it is also noted which churches and ministers are absent; but there is no mention on these rolls of the churches and ministers of other denominations in the region. The OPC possesses a formal roll including all the churches, members and officers of the OPC, but no formal roll of churches, members and officers of other denominations. (See here for more on this.)
So if the practice of fraternal relations does not imply a recognition of de jure legitimacy and authority between denominations, what does it imply? (We are, of course, assuming here that there is enough consistency in the practices of these denominations with regard to matters of church unity and authority to put forward a consistent meaning to their categories and actions in this regard. That this is the case should not be taken for granted, but it is helpful to see how far we can get assuming that the categories and practices are at least basically consistent and intelligible.) I think that what fraternal relations amounts to is basically this: "Although we do not formally recognize the de jure legitimacy and authority of your officers and church courts, yet we formally recognize that you are a denomination which teaches the fundamentals of the Christian faith, and even the core elements of the historic Reformed faith, and which seems to seek to live out such a confession in the life of your body, and on the basis of these things we formally recognize that you are truly a part of the visible Body of Christ with a faith and practice very close to ours. On the basis of this recognition, we wish to find various ways to express the unity of our faith and life while seeking to work towards full communion and a full recognition of each others' de jure legitimacy and authority."