Samuel Hudson and the London Ministers on the Difference between Presbyterianism and Independency

Samuel Hudson, in his book entitled A Vindication of the Essence and Unity of the Church-Catholick Visible (1658), cites approvingly the London Ministers who authored Jus Divinum Regiminis Ecclesiastici (The Divine Right of Church Government), a famous work defending presbyterian church government, on the difference between presbyterianism and independency (p. 125):

[T]hey [the London Ministers] only set down the difference between the Presbyterians and Independents there [in the preface to Jus Divinum] to be in this, that the Presbyterians hold that there is one generall Church of Christ on earth, and that all particular Churches and single Congregations are but as similar parts of the whole; and the Independents (say they) hold that there is no other visible Church of Christ, but only a single Congregation, meeting in one place to partake of all Ordinances.

The distinguishing characteristic of presbyterianism (at least in contrast to independency or congregationalism) is that presbyterians hold that there is a single visible catholic church on the earth, whereas independents hold that there is not one visible church on the earth (at least in a formal sense) but that there are only particular visible churches formally independent from each other.  Our modern semi-congregationalists allow for individual congregations to clump together in denominations, but, as the denominations exist independently from each other, we still have a form of independency rather than pure presbyterianism.

For more, see here, here, and here.