As I wrote in part 1, the "half Kaddish" is the "real" kaddish. Over time, various other forms of the Kaddish have developed, consisting mainly of additions to the basic "half Kaddish". These additions are custom only.  

One of these is called by Ashkenazim "mourner's kaddish", and by Sepharadim "Kaddish Yehe Shelama". This Kaddish was originally designed to be recited after public study of Scripture. It eventually found its way into the prayer service, following a section of Biblical verses. It consists of two additional paragraphs; The first paragraph in the Ashkenazi custom asking for peace from Heaven. In the Sepharadic version the first paragraph is considerably longer, asking also for life, fullness, salvation, consolation, healing, redemption, forgiveness and atonement. Followed by by a Hebrew addition (as opposed to Aramaic, the language of the rest of the Kaddish) "He who makes Peace in His Holy Habitation, may He make Peace for us and all Israel".  

Another version, designed to be said shortly after completing the 'Amidah prayer, places between the half Kaddish and the above mentioned two additions, a request that our be prayer and request be acceptable to G-d. Yet another form came in, originally to be recited after public Talmudic study, that places after the half Kaddish and before the prayer for peace, a prayer for the rabbis, and all who study the Torah, both here and everywhere else. It Ashkenazic tradition, it is known as "Rabbanan Kaddish". This, too, became part of the prayer service, following passages of Talmudic literature.  

A fifth, and far less known Kaddish is recited both after a burial, and after the completion of the study of a Talmudic tractate (siyyum). It is essentially the mourner's Kaddish, but contains additional words within the half Kaddish section; "May renew the world, rebuild His house,rebuild Jerusalem uproot idolatry; replacing it with the worship of Heaven (G-d), revive the dead..." This is the only Kaddish that actually mentions the dead. It is obviously appropriate for a funeral, but I have never seen a cogent explanation of why we say it at the celebration of completing a Tractate. In less learned communities, where it is felt that the mourners might be confused by the unfamiliar words, the regular mourner's Kaddish is substituted.  

But why so many recitations of Kaddish? Aren't the ones instituted by our Sages to separate the main parts of the prayer enough? That will be my next post.