The idea that there are two kingdoms (the civil magistrate and the church) is a distinction that goes back, in terms of historical theology, at least to Augustine (leaving aside the Biblical question, which is an important one).
There are, however, a variety of positions with respect to the two kingdoms.
The ultramontanist position holds that the bishop of Rome (over the mountains, i.e. the Alps) has supreme power of all earthly powers, both secular and religious. This attitude is expressed in Pope Boniface VIII's Unam Sanctam, which includes that famous line: “Now, therefore, we declare, say, define, and pronounce that for every human creature it is altogether necessary for salvation to be subject to the authority of the Roman pontiff.”
We, the Reformed, reject this position on a variety of grounds, including on the ground that the Roman bishop is not only not the head of the visible church, he is outside the visible church.
Whether or not Erastus himself ever held the position, the position labeled "Erastian" is a position similar to that seemingly held by the Holy Roman Emperor (at times) and by Constantine and many of the Byzantine emperors, namely that the state has power over the church.
This view was rejected by the Westminster Assembly, although apparently a small contingent of men who held such a view were present (and although apparently Parliament at the time had many members who held such a view). Perhaps my Anglican friends would not appreciate me saying this, but this position seems to be the de jure position of the Anglican church, which has the monarch as its head, although de facto the Anglican church seems to have a large degree of autonomy from Her Royal Highness (May God save the Queen!).
3. Classical Reformed
The remainder of the Reformers held a view that provided a greater level of equality and autonomy between church and state. The state does not administer the sacraments, but can call councils. The church does not have authority over the state, but it may petition the state with respect to matters that concern the church. However, the state does serve the church in a sense, in that it upholds God's law and promotes the true religion.
4. American Reformed
Some of the Americans took the position that religious freedom is a fundamental human right, and that consequently the state should give a large amount of toleration to both a variety of Christian denominations. The motivation seems to have arisen from a concern over the question of "persecuting" heretics. Later this was expanded to include a large amount of toleration even for non-Christian religions.
While I label this "American," many of the sentiments that seemingly flourished initially in America later became popular in other parts of the world. For example, the church of England subsequently revised its 39 articles to make them more inclusive with respect to those who do not hold to the classical Reformed view (or the Erastian view).
It seems that some contemporary theologians - names typically associated with Westminster West (located in Escondido, California) - are advocating a position with respect to the two kingdoms that takes matters even further away from the classical Reformed position. Their position seems to include such ideas as that the American "blue laws" related to the Lord's day, criminal punishment for adultery, and the like are not proper. The position appears to reflect an idea that there should be a radical separation of church and state, and consequently is sometimes referred to as "r2k," although the adherents of the position do not appreciate that label.
I say "seems to include," because there does not appear to be a lot of clear positive statements of their positions. I wonder if any of my readers know of, and can locate for me, their positive Biblical or logical argument for their position. I can find this sort of thing with respect to the American Reformed position, and I can find very excellent works ably defending the classical Reformed position, but I cannot locate anything of substance for the Escondido position.
Various people have argued that civil government is intrinsically evil, and that consequently Christians should not be involved in any way in civil government. Certain sects, such as the Amish, are known for holding to such a position. However, it should be understood that such a position is clearly contrary to Scripture.