Rhema and Logos are two Greek words meaning ‘word’.
The traditional Pentecostal teaching goes something like this: ‘Logos’ means written word, and ‘Rhema’ means dynamic utterance. Applied to questions of discerning the voice of God, what we want is to hear the specific-to-our-situation Rhema word of God — and then test it by proven biblical ‘Logos’ principles to ensure that it is indeed a sound God-given directive.
The more conservative Evangelical teaching is traditionally unconvinced by this position. They argue that the Greek words ‘Logos’ and ‘Rhema’ cannot consistently be distinguished the way that the Pentecostals claim. And they use this to justify their stance that waiting on God for a personal ‘Rhema’ word is hypercharismatic nonsense, and that all we can faithfully do is study to work out how best to apply the biblical ‘Logos’ principles to any given situation.
My personal position is that while I’m happy to accept that linguistically ‘Logos’ and ‘Rhema’ might not consistently function in NT Greek the way that Pentecostals now use the words, nevertheless it is a very helpful theological distinction.
And I would even suggest that we can also paint a broad brushstroke picture of Liberal Christians’ behaviour here. Whereas Pentecostals believe in Rhema and Logos, using Logos to test Rhema, and Rhema to direct Logos; and Conservative Evangelicals believe only in Logos; Liberals (perhaps) believe in Rhema but not Logos: that is, they continue to believe that as they stay in a position of prayerful openness to God, they can experience His guidance but have lost confidence in the reliability of biblical principles by which to test this sense of guidance. And thus they are in danger of being swept away on the currents of whatever contemporary society feels most strongly.
Oh, and here is a more thorough example of the classic teaching.