Halliday & Matthiessen (1999: 466, 467):
… a process is both an organiser of participants and an event that is instantiable in time. These two perspectives lead to different criteria for establishing process typologies. For example, will have left is the Process part of they will have left the house by now, where it organises the participants they and the house; but it also has internal organisation as an event will —> have —> left: see Figure 12-1.
The two perspectives are associated with different grammatical units, the clause (for the participant organising perspective) and the verbal group (for the temporal instantiation).