[Not written yet.]
In the system of three souls, the Soul Neshamah (נשמה) covers the worlds Briah and Atziluth, which are the Supernal Sephiroth Binah, Chokmah, and Kether. In the system of four souls, Neshamah covers only Briah, with the Soul Chiah covering Atziluth; whereas in the system of five souls Neshamah equates only with Binah, with Chiah covering Chokmah and the Soul Yechidah covering Kether.
Who's right? Who can say? Personally, I favor the model of five souls. You can read my sketch of the Souls to see why I think this way. However, Sefer Zohar discusses only the three (Nephesh, Ruach, and Neshamah), though discussions around Zohar talk about the other two. In exactly the way the Supernal Triad is a complex three-in-one arrangement, it is possible to consider Neshamah as being an amalgam of Neshamah, Chiah, and Yechidah. See the article on Soul for more information.
The souls are divided from one another by veils. This group sits above the Abyss, separating it from the soul Ruach. Within this group[1] there is another veil, the Presence of the Most High, separating Briah from Atziluth (or, looked at another way, duality from non-duality).