It's when I play guitar or bass with a vocalist or another instrumentalist, just the two of us...though not necesseraly we play Bill Wither song :)
When playing with a non-chordal instrument/melodic instrument (an instrument that only sounds a note at a time, such as: vocal, saxophone, trumpet, etc.), I usually play the role as a rhythm sectionist that provide the chords & groove, where else the vocalist/saxophonist/trumpeter has control over the melody.
When playing with another chordal instrument, such as: keyboard, bass, guitar, etc; both instrument can take turn to be the rhythm sesionist (chords & groove) and melody player.
Playing duet with a percussionist is also unique combination as it enhance the guitar's groove while the guitarist/bassist is still in full control of harmony & melody.