Presbyterianism is first of all a governmental framework. Its governmental bodies, when called to the work, are a graded system of courts. The individual Christian or church-member is not left solely to dictates or judgments of one or even a few of his leaders, at the congregational level. Depending on how much "church" is contained within a denomination--if for instance there are sessions, presbyteries, and a general assembly--theoretically there exists a "right of appeal" within the justice-system on earth, whereby decisions of fallible men may be reviewed once or even twice, so as to have the whole church speak with clarity to an issue.
The difference would be, that in a congregational church, an individual who has been judged and has no further to take his sentence, has one appeal--to Jesus Christ on Judgment Day. The decisions of pastors and elders or deacons (or perhaps the congregation) is final in his case. If the church is simply a voluntary association, then those who run the place (whether individually, by board, or by a collective whole) ultimately decide who stays and who goes. The single congregation is "the whole church." No one owes anyone beyond it anything except to Christ on Judgment Day.
Conceptually, the diverging answers to the question turn on the nature of "the church" on earth. Is there anything that is justly called "a church" that does not meet under one roof, or sit under one man's preaching, or move under direction of one board of a directly-elected body having immediate authority over the voters? Congregationalism says "no." There is one "layer" of authority (maybe thicker or thinner, depending on the church or bylaws) between the individual and Christ. Presbyterianism says "yes" (basically). There may be cases where there is one layer (actually, or for all intents and purposes); but there is also a whole, visible "church on earth," which expresses the idea of one government for that whole, under Christ, and not atomized between perfectly autonomous bodies.
So, the SBC is a Convention of churches (the capital "C"). There isn't any such entity as "the SouthernBaptistChurch." But there IS such a thing as "the OrthodoxPresbyterianChurch." Now, the URC puts its name in the plural, "the UnitedReformedChurches," but the government is still presbyterian and it exercises a common authority. Their name simply emphasizes the reality (which is also found in the OPC) that the congregations are as much "the church" as the larger. A noticeable difference between Presbyterian and Reformed church polity is where a minister's basic membership is located--in a Presbyterian church, the minister's membership is in the "regional church," whose governing body is the presbytery; whereas in Reformed polity, ministers are members of the particular congregations they serve. The idea of "regional" or "national" church is foreign to congregational principles.
Practically, in our day there is very little practical matter that is dictated to particular congregations from their parent presbytery or classis. Our presbyterian churches are rather "congregational" in terms of self-awareness and local government. There's some good "jealousy" for the rights of sessions to direct their own affairs. The Presbytery is especially concerned with doctrinal fidelity in the body, besides judicial oversight and support mechanisms in problem situations at the particular level. In the end, we understand that "the church" exists whole and entire in the congregation, as well as whole and entire in every larger gathering of the church(es).