Halliday & Matthiessen (2004: 344):
The difference between this [System III] and System II is that in System III the effect is simply to eliminate the entire choice of primary tense. System I minus the α tense gives System III. The non-finite or modalised verbal group has no deictic tense element: non-finites because they have no deictic at all (that is what non-finite implies: not anchored in the here-and-now); modalised because, while they have a deictic element (being finite), their deixis takes the form of modality and not tense. Strictly speaking, the first secondary tense of the non-finite should be labelled α, since that becomes the Head element; but it seems simpler and clearer to retain the association of α with finiteness and show non-finites as beginning with β.