If you browse through
http://www.ayahuasca-info.com you'l find all the information you need, and more.
To answer your question in a nutshell:
There is (1) a vine called ayahuasca, and (2) a brew named ayahuasca, or yage.
The vine itself contains natural MAO-inhibitors. It doesn't contain DMT and thus is not psychedelic in itself. Other plants contain DMT, and when the vine is combined with any of these plants, that combination is called ayahuasca. DMT-containing plants need to be accompanied by an MAO-inhibitor to be orally active.
There are some plants that have been used traditionally, and there are some that have been discovered recently. On the Azarius ayahuasca page you find all of these plants.
As I write this 15 grams of Mimosa hostilis (Jurema Preta) is boiling on my stove, which I will drink in an hour, together with 3 grams of Peganum harmala (Syrian Rue). Though there is no ayahuasca vine in this brew, it will have similar effects to the traditional yage.
I prefer the Peganum harmala & Mimosa hostilis combination for the following reasons:
Much cheaper per dose.
Much easier to prepare.
Much more gentle on the stomach.