In American Presbyterianism, is the Presbytery the collection of elders alone or the churches in that region as well? In other words would I say that my church is in the Philadelphia Presbytery or just my session?
This is the OPC's perspective. We are "big" on terminology, on paper anyway. In everyday parlance, the lines are as blurred as anyone else'. The below definitions come out of the OPC BCO.
The individual congregations of the OPC are clustered in "the regional church." This is our way of saying that the church, in one significant respect, is singular. The denomination is the OPC, not the OPCs. Compare this name to the URC, in which that last letter is plural, deliberately so. I'm not saying either one is wrong; it is a noticeable difference.
Each self-governing congregation is THE church, a manifestation of Christ's body. So, you can find THE church wherever you find a faithful congregation. Our church-extension efforts--missions--are not self governing; they are not mature. If the work is an extension of a single congregation, the members present there are enrolled on the mother-church, until they be transferred. If the work is an extension of the regional church, the members are enrolled on the roll of the regional church, until transferred to the roll of the organized congregation, having its own elders.
We typically take the formal step of authorizing an unorganized mission (without its own session) to use the OPC name for the purposes of identification and advertising. We want to publicize our effort to put the presence of the church in some place. In any case, the reality is that the people gathering there are enrolled in the church, in an OPC manifestation.
In the OPC, the regional church in one place joins with the regional church in other places to form "the whole church." Its hard to call it a "national church" when there are congregations in Canada. The point being, that wherever the church gathers, there you should find THE church.
So what exactly is "the Presbytery? In OPC terminology, "The presbytery is the governing body of a regional church," see BCO 14.2. It corresponds to the Session of the local church, or the General Assembly of the whole church. The BCO continues concerning the composition of Presbytery: "It consists of all the ministers and all the ruling elders of the congregations of the regional church." No mention there (as in the definition of "regional church") of the particular congregations, with their associated mission works, or the mission works and members directly overseen by the regional church.
Furthermore, you will note that the Presbytery will be comprised of all the ministers (whose original jurisdiction is that governing body; they are enrolled in the regional church), as well as elder-commissioners from the particular churches.