Though i really urge you to read the entire thing, here is an excerpt from Adeu Rinpoche's explanation:
When embarking on meditation practice in the Mahamudra tradition, the meditator is taught three aspects: stillness, occurrence and noticing.
The cultivation of stillness means to train in cutting off involvement in memories; you disengage from entertaining any thought about what has happened in the past. The same with regard to the future: you are not supposed to construct any plans about the next moment. And in the present, right now, simply and completely let go. Drop everything and settle into nowness. In the Mahamudra tradition, stillness refers to not following thoughts about the past, present or future--not churning out any new thoughts.
A beginner will notice that totally letting be without any thought involvement does not last that long. Due to the karmic force of the energy currents, new thoughts are continuously formed--thoughts grasping at subject and object, at the pleasant and unpleasant. The activation of such patterns is known as occurrence.
When the attention is quiet and still, there is a knowing that this is so. When one is involved in thinking about this and that, there is a knowing that this is so. In this context of stillness and thought occurrence, this knowing is called noticing. [...] As you grow more capable, there comes a point when the thought occurrences no longer have such a strong hold on the attention. It becomes easier to arrive back in quietness. Eventually, every time a thought begins to stir, rather than getting caught up in it, you will simply be able to remain, until the force of the thought occurrence weakens and the aware quality grows and strengthens. The dividing line between stillness and occurrence fades away. That is the point at which we can recognize the actual identity of noticing what mind nature really is. In other words, vipashyana can begin. [...]
In the beginning, a thought vanishes; that is called stillness. Next, a new thought arises; that is called thought occurrence. One notices that these are happening. These three--stillness, thought occurrence and noticing--have to do with becoming increasingly aware of the gap between thoguts. This aware quality grows stronger and stronger, which only happens with training. You cannot artificially increase it. The difference between shamatha and vipashyana, in this context, is when you recognize that which notices and what the awake quality is.
According to the Dzogchen system, if your shamatha practice is simply training in being absentminded remaining in a neutral, indifferent state without any thought activity whatsoever, this is known as the all-ground. It is simply a way of being free of thought involvement. Moreover, when attention becomes active within the expanse of the all-ground that activity is known as dualistic mind. But when the dividing line between stillness and thought occurrence fades away, and instead the strength of the aware quality is intensified, the awake quality is known as rigpa. Depending on whether one is using the Mahamudra system or the Dzogchen approach, there are different terminologies, but the actual training is essentially the same in both cases
According to Dzogchen one must identify the ground of liberation, the natural state of rigpa, which is not the same as the ordinary state of mind known as the all-ground. No matter how many thousands of years one trains in the state of the all-ground, there will be absolutely no progress--one will simply arise again in the state of samsara--whereas training in the antural state of mnd of rigpa is nothing other than the ground of liberation. There it is important to distinguish the normal, ordinary mind of the all-ground from the antural, ordinaary mind that is the ground of liberation, and train accordingly. To put it simply, according to Dzogchen the self-knowing original wakefulness is pointed out in our ordinary state of mind.
According to Mahamudra, the essence of the meditation practice is found within the ordinary, natural state of mind; it is pointed out as the original, true wakefulness. Having recognized this, one can then proceed to train in it, and as the training deepens, there are certain stages of progress described as the four yogas, each of which is further divided into the three categories of lesser, medium and higher capacity. These are collectively known as the twelve aspects of the four yogas of the path of Mahamudra. Another approach is to apply the structure of the four yogas to each of the yogas, resulting in sixteen aspects. These are equally valid and merely describe the ever-deepening levels of experience and stability in the natural, ordinary mind.
The Dzogchen path has a similar explanation. According to trekcho, there is a growing sense of becomeing more and more accustomed to the state of rigpa, which is described as the stages of the path known as the four visions. These four can also be applied to the practice of togal.
But whether you follow Dzogchen or Mahamudra, please understand that ultimately there is no real difference. There is not one awakened state called Mahamudra and a separate one known as the Great Perfection. It is all of one taste within the expanse of dharmakaya. What these two words actually refer to is the basic nature of all things. Since all phenomena, all that appears and exists within samsara and nirvana, have the stamp of great bliss, it is called "the Great Seal," which is the literal meaning of Mahamudra. Similarly, since all phenomena are perfected in the expanse of self-existing awareness, it is called Dzogchen, Great Perfection.
also just to clarify the issue of "sudden" versus "gradual" in the context of Dzogchen:
The Dzogchen path begins with the actuality of rigpa being pointed out. This is like being shown the beginning of the road. One should not just stand there and wait, but must move forward. Sometimes people misunderstand and think that having received the pointing-out instruction and recognized rigpa in one's experience is enough and that they have achieved all there is to achieve. It is not sufficient however. Recognizing rigpa is only the beginning of the Dzogchen path. We need to follow through, and it requires a lot of perseverence. Giving the pointing-out instruction is like pointing to the ground and saying, "This is the road to Lhasa." If you just stand there, you will never get to Lhasa. You need to proceed step by step along the road, putting one foot in front of the other. Similarly having recognized rigpa, you need to train and progress along the path. Of course you could say that the perseverance is effortless, however this definitely does not mean that we should ignore the need for practice.