One of the things that I think causes enormous confusion in trying to understand the positions of the various Presbyterian and Reformed churches in terms of their relationships to one another is that many of those who hold to the presbyterian model of church government today seem to hold it with a bit of confusion, with a significant amount of influence from independency or congregationalism.
More particularly, many Presbyterians today seem to have sort-of adopted a model of church government that might be called semi-presbyterianism or semi-congregationalism, or, as I like to call it, "clumpy congregationalism." Historic congregationalism, or independency, holds to a system where formal church authority functions only at the level of individual congregations. Beyond the local congregation, there may be confederacies of various sorts, but there are no assemblies with any binding authority. (In practice, various congregationalist bodies work out the details of this in a variety of ways, some closer and some farther away from presbyterianism.)
Many modern Presbyterian churches seem sometimes to be functioning under a modified or expanded version of congregationalism, where presbyterian rules of church governance are enforced up to a certain point, and then the polity switches to a congregationalist sort of system.
For example, in the OPC, there is a firm commitment to presbyterian principles of church government. Congregations are not autonomous or independent, but are united together under higher binding formal councils. Groups of local congregations in a region are united together under presbyteries, which exercise governance over those congregations. These presbyteries are, in turn, united together under the General Assembly, which exercises governance over all the OPC presbyteries. The General Assembly is the highest binding church court recognized in the OPC. Now, according to the presbyterian system, the concentric circles of church courts ought to continue to expand until all the churches in the world are under an ultimate binding ecumenical council (see the quotation from the Second Book of Discipline of the Church of Scotland found at the bottom of this article). So the fact that the General Assembly of the OPC is the highest judicatory in the OPC ought to mean that the OPC recognizes only the OPC as constituting the entirety of the de jure visible church of Christ in terms of its formal structures of authority. And the OPC does indeed make clear that it does understand and hold to the presbyterian system all the way up to the logical conclusion that "[t]he ultimate goal of the unity of the church is nothing less than one world-wide presbyterian/reformed church."
However, I have had numerous conversations with individuals, including ministers, in the OPC who seem to think that denominational division is a perfectly acceptable situation and that it does not at all imply any rejection of the de jure authority or legitimacy of bodies from whom denominational separation is maintained. I have recently spoken to one OPC minister who maintains that the OPC fully recognizes the de jure authority of other Reformed denominations and that denominational separation is really no more inherently sinful or problematic than jurisdictional distinctions between congregations and presbyteries within a single denomination. He holds that the separation between, say, the OPC and the RCUS is really, in principle, the same kind of separation that exists between different presbyteries within the OPC. Like the latter, the former is not a schismatic wound to the unity of the church of Christ but merely a matter of distinction for logistical jurisdictional purposes. Just as presbyteries remain distinct from each other for logistical purposes while maintaining full unity, so the OPC and the RCUS remain distinct from each other for good practical reasons while maintaining full unity.
But this is absurd, and a rather remarkable failure to recognize both reality and the full implications of presbyterian church government. For one thing, the OPC and the RCUS are not divided along regional lines. It makes sense for logistical purposes to distinguish presbyteries from each other along geographical lines. But RCUS and OPC congregations are frequently mixed together in the same regions. When an OPC presbytery invites all the ministers of the OPC churches within a certain designated region as full voting members to its meetings, it cannot plead that its exclusion of RCUS ministers within that same geographical boundary is owing to nothing more than jurisdictional distinctions for logistical purposes. And, even more importantly, while all the OPC churches ultimately find formal unity in that they are all eventually subject to a common binding umbrella council, the same cannot be said for both the OPC and the RCUS churches. These churches never do find any union in any common binding council. So to pretend that such denominational separations are of the same sort as distinctions among the jurisdictions of presbyteries within a single denomination, is, frankly, evidently ludicrous.
And it is also a betrayal of true presbyterian church government for a semi-presbyterianism or a semi-congregationalism. Whereas traditional conregationalism maintains that the visible church of Christ does and should consist of a bunch of autonomous congregations under no higher binding authority that unites them together, so the view I just described above basically holds that the visible church of Christ does and should (at least sometimes) consist of a number of "clumps" (hence my term "clumpy congregationalism") of churches, which churches are united to each other by means of a presbyterian system but which clumps are only united to the other clumps in congregationalist ways. So what we have, basically, is a big, loose association (such as NAPARC or the ICRC) which is held together by congregationalist methods (councils with non-binding authority) and which consists of a bunch of clumps of churches held together by presbyterian church government (such as the OPC, the RCUS, the PCA, etc.). It is as if we have a giant congregationalist denomination in which we find a plethora of presbyterian "clubs" which various officers and members of the larger church may be a part of (and, indeed, are required to be members of one of them, whichever they may choose).
This is certainly not presbyterianism. What is the OPC, for example? In a presbyterian system, the OPC must be either nothing other than the de jure catholic church or it is a schismatic sect. There is no place in the Scriptural view of the church for something like the OPC considered as a part, but not the whole, of the catholic church. Where in Scripture do we find license for the one church of Christ to divide itself up into clumps of churches with distinct names that function by-and-large separately from each other in their formal functions? Where does Scripture give the right to form little cliques inside the catholic church that get to have their own separate church courts and exclude each other formally from them? This is a serious betrayal of the Scriptural view of the unity of the church of Christ. It is the partial victory of congregationalism, a view historically firmly rejected by the Reformed churches. (And even now, many Presbyterian churches, such as the OPC, formally reject it and adhere in confession to full presbyterian church government, while maintaining within them many who hold serious confusion on this point and who influence the church into a lethargy that fails to deal adequately with the seriousness of denominational divisions in the church of Christ).
For more, see here and here.