The modality of Chant as it has been received is complicated as the early chant was "corrected" to fit later modal theories, like Guido d'Arezzo's Gamut.

As you probably know, the chant was first and foremost an unwritten, oral tradition, the first layer of musical notation is a series of symbols showing the rough contour of the melody, without staff lines, and, intended as a memory aid to those who already knew the chant. As the method of notating exact pitches developed, the pitches within the chant became more rigidly fixed to the pitches of the diatonic Gamut, with various microtones, "accidentals", etc., being lost.

Because the Guidonian pitch system only permits one accidental: b-flat (fa), and that only from the second octave of the Gamut (the lowest B can only be natural (mi) in the Guidonian system), if a chant in the sixth mode (usually in F) requires the note below the final to be flattened (E-flat), then the chant has to be written transposed from F to c so that the b-flat can be used, because the note E-flat doesn't exist in the Gamut. For convenience's sake, modern books have a transposed version of the mode 6 Psalm tone, Tone 6c, which is used with these transposed melodies, but the tone doesn't differ in any way from the regular mode 6 tone, Tone 6F.

The Liber Usualis (p. 211) gives tone 6F or 6C for the Magnificat, the only difference being the clef, as is also the case with Tone 2D and 2A (p. 208).