Let's Play "Pin the Denomination on the De Jure Visible Church."

The Second Book of Discipline of the Church of Scotland well sums up the presbyterian nature of the church.  Take a look at the outline below of the various parts of the one visible church of Christ de jure, and figure out where your denomination's general assembly (or synod) fits into it. Then pick another denomination and figure out where it fits into it.  After you do this, read what I say below the outline.

Chapter 7 - Of the Elderships, and Assemblies, and Discipline

1. Elderships and assemblies are commonly constituted of pastors, doctors, and such as we commonly call elders, that labour not in the word and doctrine, of whom, and of whose several power has been spoken.
   
2. Assemblies are of four sorts. For, either are they of particular kirks and congregations, one or more, or of a province, or of a whole nation, or of all and diverse nations professing one Jesus Christ.
   
3. All the ecclesiastical assemblies have power to convene lawfully together for treating of things concerning the kirk, and pertaining to their charge. They have power to appoint times and places to that effect; and at one meeting to appoint the diet, time, and place for another.
   
4. In all the assemblies a moderator should be chosen (by the common consent of the whole brethren convened) who should propose matters, gather the votes, and cause good order to be kept in the assemblies. Diligence should be taken, chiefly by the moderator, that only ecclesiastical things be handled in the assemblies, and that there be no meddling with anything pertaining to the civil jurisdiction.
   
5. Every assembly has power to send forth from them of their own number, one or more visitors to see how all things are ruled in the bounds of their jurisdiction. Visitation of more kirks is no ordinary ecclesiastical office in the person of one man; neither may the name of a bishop be attributed to the visitor only; neither is it necessary to abide always in one man's person; but it is the part of the eldership to send out qualified persons to visit pro re nata.
   
6. The final end of all assemblies is, first, to keep the religion and doctrine in purity, without error and corruption; next, to keep comeliness and order in the kirk.
   
7. For this order's case, they may make certain rules and constitutions appertaining to the good behaviour of all the members of the kirk in their vocation.
   
8. They have power also to abrogate and abolish all statutes and ordinances concerning ecclesiastical matters that are found noisome and unprofitable, and agree not with the time, or are abused by the people.
   
9. They have power to execute ecclesiastical discipline and punishment upon all transgressors and proud contemners of the good order and policy of the kirk; and so the whole discipline is in their hands.
   
10. The first kind and sort of assemblies, although they are within particular congregations, yet they exercise the power, authority, and jurisdiction of the kirk with mutual consent, and therefore bear sometimes the name of the kirk. When we speak of the elders of the particular congregations, we mean not that every particular parish can, or may, have their own particular elderships, especially to landward; but we think three or four, more or fewer, particular kirks may have one eldership common to them all, to judge their ecclesiastical causes. Albeit this is meet, that some of the elders be chosen out of every particular congregation, to concur with the rest of their brethren in the common assembly, and to take up the delations of offences within their own kirks, and bring them to the assembly. This we gather from the practice of the primitive kirk, where elders, or colleges of seniors, were constituted in cities and famous places.
    
11. The power of these particular elderships is to give diligent labours in the bounds committed to their charge, that the kirks be kept in good order; to inquire diligently of naughty and unruly persons, and travail to bring them in the way again, either by admonition, or threatening of God's judgments, or by correction.
    
12. It pertains to the eldership to take heed that the word of God be purely preached within their bounds, the sacraments rightly ministered, the discipline rightly maintained, and the ecclesiastical goods uncorruptly distributed.
    
13. It belongs to this kind of assembly to cause the ordinances made by the assemblies provincial, national, and general, to be kept, and put in execution; to make constitutions which concern to; prevpon[2] in the kirk, for the decent order of these particular kirks where they govern; providing they alter no rules made by the general or provincial assemblies, and that they make the provincial assemblies foreseen of these rules that they shall make, and abolish them that tend to the hurt of the same.
    
14. It has power to excommunicate the obstinate.
    
15. The power of election of them who bear ecclesiastical charges pertains to this kind of assembly, within their own bounds, being well erected and constituted of many pastors and elders of sufficient ability.
    
16. By the like reason their deposition also pertains to this kind of assembly, as of them that teach erroneous and corrupt doctrine; that are of scandalous life, and, after admonition, desist not; that are given to schism or rebellion against the kirk, manifest blasphemy, simony, corruption of bribes, falsehood, perjury, whoredom, theft, drunkenness, fighting worthy of punishment by the law, usury, dancing, infamy, and all others that deserve separation from the kirk. These also who are found altogether insufficient to execute their charge should be deposed; whereof other kirks would be advertised, that they receive not the persons deposed.
    
17. Yet they ought not to be deposed who, through age, sickness, or other accidents, become unmeet to do their office; in the which case their honour should remain to them, their kirk should maintain them; and others ought to be provided to do their office.
    
18. Provincial assemblies we call lawful conventions of the pastors, doctors, and other elders of a province, gathered for the common affairs of the kirks thereof; which also may be called the conference of the kirk and brethren.
    
19. These assemblies are instituted for weighty matters, to be treated by mutual consent and assistance of the brethren within the provinces, as needs requires.
    
20. This assembly has power to handle, order, and redress all things omitted, or done amiss, in the particular assemblies. It has power to depose the office-bearers of that province for good and just causes deserving deprivation. And, generally, these assemblies have the whole power of the particular elderships whereof they are collected.
    
21. The national assembly, which is general to us, is a lawful convention of the whole kirks of the realm or nation where it is used and gathered for the common affairs of the kirk; and may be called the general eldership of the whole kirk within the realm. None are subject to repair to this assembly to vote but ecclesiastical persons, to such a number as shall be thought good by the same assembly; not excluding other persons that will repair to the said assembly to propose, hear, and reason.
    
22. This assembly is instituted, that all things either omitted or done amiss in the provincial assemblies may be redressed and handled; and things generally serving for the weal of the whole body of the kirk within the realm may be foreseen, treated, and set forth to God's glory.
    
23. It should take care that kirks be planted where they are not planted. It should prescribe the rule how the other two kinds of assemblies should proceed in all things.
    
24. This assembly should take heed that the spiritual jurisdiction and the civil be not confounded to the hurt of the kirk; that the patrimony of the kirk be not diminished nor abused; and, generally, concerning all weighty affairs that concern the weal and good order of the whole kirks of the realm, it ought to interpose authority thereto.
    
25. There is, besides these, another more general kind of assembly, which is of all nations and estates of persons within the kirk, representing the universal kirk of Christ; which may be called properly the general assembly, or general council of the whole kirk of God. These assemblies were appointed and called together specially, when any great schism or controversy in doctrine did arise in the kirk, and were convoked at the command of godly emperors, being for the time, for avoiding of schisms within the universal kirk of God; which, because they appertain not to the particular estate of one realm, we cease further to speak of them. 

Did you try to find your denomination plus another one in there?  Hopefully you noticed that it is impossible.  This outline does not have any room for multiple de jure denominations.  That is because presbyterianism has no room for multiple de jure denominations.  The idea of there being multiple de jure denominations is not presbyterian but semi-congregationalist in nature. Multiple denominations don't fit because the church courts of different denominations are independent from each other, while presbyterianism does not allow for independent church courts in the visible church.  Also, different denominations usually have somewhat different standards of doctrine and practice.  And yet presbyterianism requires that purity of faith and practice be preserved by the eldership of the church. Sessions keep local congregations pure, presbyteries keep churches under them pure, national assemblies keep churches under them pure, and ecumenical or general international assemblies keep national churches under them pure.  This system does not allow for purity to be kept only at the presbytery level or the national level while divergence from purity is tolerated beyond it.

If we want to be presbyterian in the manner of the Second Book of Discipline, we are going to have to rethink much of what we do in the modern Reformed world.

For more, see here and here.