Madhyamaka = the Middle Way school of Buddhism.
Yogachara = Mind Only school of Buddhism
Here is a good article that explains the Four Schools of Buddhism from a Tibetan point of view:
http://www.khandro.net/doctrine_philo_views.htm
The major point of the dominant school of Madhyamaka - Prasangika (the implication school) - is to stop striving and drop everything.
The major point of Yogachara is to affect the transformation of our mind to that of the Buddha nature.
One can't really say that Madhyamaka is Prasangika, because actually all of Buddhism should be the Middle Way - whatever that is (see this post for more info on the Middle Way). The reason why some people see Prasangika as Madhyamaka is because of the political dominance of the Gelugs in Tibet (which is the school of the Dalai Lama). However, there are other schools which have other versions of the Madhyamaka as Yogachara, especially the Nyingma school.
I personally love the Yogachara approach, although I think Dudjom Rinpoche (a Tibetan master from the Nyingma school) explained it best:
The Madhyamaka of the Prasangika and the Svatantrika is the coarse, Outer Madhyamaka. It should indeed be expressed by those who profess well-informed intelligence during debates with extremist Outsiders, during the composition of great treatises, and while establishing texts which concern supreme reasoning. However, when the subtle, inner Madhyamaka is experientially cultivated, one should meditate on the nature of Yogacara-Madhyamaka.
As to what all of this has to do with Zen is another story. Zen is the meditation tradition of Japan, built upon the Chan tradition of China, built upon the "Dhyana" tradition of Indian Buddhism. So you can imagine how this changed and flowed as it moved from country to country. Dhyana means meditation, and it is cultivated in all schools of Indian Buddhism, and probably in just about every school of Buddhism period. Chan and Zen just put an exclusive emphasis on it.
Both Prasangika Madhyamaka and Yogachara have Dhyana meditation in them, although one could argue that Yogachara is more focused on meditation than Prasangika.
My understanding is that the the Mind-Only or Yogacara (sometimes called Cittamatra) essentially holds that all external phenomenon are just manifestations of mind.
The Middle Way or Madhyamika school essentially suggests that even mind itself is a manifestation which is dependent on your own past deeds (karma).
There are many interpretations of these schools. The Madhyamika itself has a Svatantrika school within it that has two divisions within that division. It also has a division called the Prasangika school. The interpretations of these schools vary radically in some cases.
This link on the Middle Way that Maizuru supplied you with above may help. It may also confuse you further.