This is an illustration and summary of the various confessions derived from Westminster.
Blue - Presbyterian
Green - Congregationalist
Orange - Baptist
The Westminster Confession of Faith (WCF) was produce by the Westminster Assembly between 1644 and 1646. The confession does not outline a form of government, but the Assembly was mostly Presbyterian and would produce The Form of Presbyterial Church Government in 1645, during the drafting of WCF.
Congregationalism - the polity and the tradition - was being formulated at the same time. The "five dissenting brethren" of the Assembly produced "An Apologetical Narration" to parliament detailing their preferred form of church government, and The Cambridge Platform would be finished in Massachusetts in 1648. Congregationalists meeting at Savoy Palace in London, 1658, would draft their revision of WCF called The Savoy Declaration. It is the de facto confession of Congregationalism.
The unrevised 1646 WCF was already adopted in 1648 with the Cambridge Platform. In 1680, however, at the Reforming Synod of Boston, the messengers and elders of that synod chose to adopt the Congregationalist recension of Savoy with slight alteration. This version would also be adopted in Connecticut as part of the 1708 Saybrook Platform, and is therefore called the Saybrook Confession.
Back in London, the Baptist movement (Congregationalism minus paedobaptism) chose to replace its 1644 "First" London Confession with their own version from the Westminster family, a revision of Savoy now called the Second London Confession (SLC). When the Philadelphia Baptist Convention produced their own revision of SLC, it took the name Philiadelphia Confession.
When the Presbyterian Church in the United States of America was eventually formed in 1789, it made its own revisions to Westminster. This revision does not have its own name, but is generally called the "American Revision." It especially addresses the chapter dealing with the magistrate, which was a key issue after the American Revolution.