Thus, it is not only important to distinguish between the institutions of church and state, but the source of each institution's guidance, and the definition of the purposes of each must be identified. It is not even enough to say that the goals of the state are temporal, and of the church eternal. It must be added that the sources of guidance and purposes are dramatically different. The essential interests of one are not the same as those of the other. As our confession defines the purpose of the state: "It is the duty of civil magistrates to protect the person and good name of all their people" (WCF 23.3). Rulers are not tasked with promoting or enforcing the "true religion." They are called to maintain civil order for all of its citizens, including Muslims, Jews, and atheists; and special revelation commands Christians to support them in this distinct endeavor.And, more specifically:
Civil magistrates may not assume to themselves the administration of the Word and sacraments; or the power of the keys of the kingdom of heaven; or, in the least, interfere in the matter so faith. Yet, as nursing fathers, it is the duty of civil magistrates to protect the Church of our common Lord, without giving the preference to any denomination of Christians above the rest, in such a manner that all ecclesiastical persons whatever shall enjoy the full, free, and unquestioned liberty of discharging every part of their sacred functions, without violence or danger. And, as Jesus Christ hath appointed a regular government and discipline in his Church, no law of any commonwealth should interfere with, let, or hinder, the due exercise thereof, among the voluntary members of any denomination of Christians, according to their own profession and belief. It is the duty of civil magistrates to protect the person and good name of all their people, in such an effectual manner as that no person be suffered, either upon pretence of religion or of infidelity, to offer any indignity, violence, abuse, or injury to any other person whatsoever: and to take order, that all religious and ecclesiastical assemblies be held without molestation or disturbance.
That said, the points of these passages seems to be the protection of the church against state interference. Back in the day, with the Anglican and Catholic churches, there were strong ties between church hierarchy and civil government. A religions like the minority Presbyterians would seem to be interested in either severing these ties or at least ensuring the civil authorities didn't cross the church/state line into the church's authority.
What these don't address is how Presbyterians should behave in the realm of civil government, when they are in fact in charge. I've found at least one area (capital punishment) where the church gives specific instruction of an area of civil government.