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.