reflecting with Gerhard:
The one Church may be regarded under different aspects:
1. As invisible
a. insofar as she always encompasses the total number of elect, some of whom are already gathered into the heavenly Kingdom and some of whom have not yet been born, so that she will only "appear" at the Last Day;
b. insofar as human eyes cannot distinguish in the visible assemblies of the church those who are saints from the non-saints, but who will be finally separated on the Last Day.
2. As visible
a. insofar as the elect are invariably found in the assembly of the called and gathered.
b. insofar as there are certainly times when the visible church is blessed with a pure doctrine, a faithful ministry, and godly divine worship, even in this age; but that this is not always the case.
Further, when dealing with the Church we may note the distinction between triumphant and militant; and when dealing with the militant between particular churches in specific places which are either pure or corrupted (though in corrupted churches God is also at work to save insofar as they retain enough of the Gospel to bestow faith and so unite poor sinners to the Blessed Trinity) as regards their teaching; yet it is possible for EVERY visible church to be corrupted, as will no doubt happen in the Great Apostasy foretold in Scripture.
And that's about as far as I've gotten in Gerhard. More to come later...