I would say leadership and discipline distinguishes an army from an armed mob. I can imagine a bunch of trained people without leaders or with leaders but without the discipline to follow them, and in both cases, I’d call that an armed mob rather than an army. Similarly, I can imagine a bunch of disciplined people with good leaders who would act like an army rather than like a mob. I also suspect that unless you have a rather unusual bunch of people in your group, it would usually require all three properties (training, leadership, and discipline) to act like an army rather than an armed mob.