First off you need to understand that, for better or worse, the Nazi state did not have clearly defined borders of responsibility. The constant struggle for influence and control between rival organizations was very much inbred into the system.
This included the Chancelleries at the very top of the state: The Reichskanzlei (Reich Chancellery), assigned to the Chancellor (head of government). Then there was the Kanzlei des Führers, Hitler's personal chancellery as "Führer". The third was the Party Chancellery, originally the "Staff of the Deputy Führer" when Rudolf Hess still held that position (1933-1941), which was mainly the joint between the government and the Nazi party. Hess was, in that function, literally a "minister without department".
Following Hess' unauthorized flight to Great Britain, Hitler abolished the position of Deputy Führer itself, renamed the "Staff of the Deputy Führer" into Party Chancellery, and appointed the man who had basically been doing all the work already, Martin Bormann, as head of the Party Chancellery (with the rank of minister). Under Bormann, the Party Chancellery grew in importance and influence to rival, and possibly eclipse, the Reich Chancellery.
Note that Hitler's position of "Führer" united three functions -- president, chancellor, and head of the NSDAP. In his testament, he separates these positions again. Quoting that document:
Reichspräsident: D ö n i t z
Reichskanzler: Dr. G o e b b e l s
Parteiminister: B o r m a n n
Since there was no "Führer" anymore, the Reich Chancellery falls back to the Chancellor, and the Party Chancellery remains in Bormann's hands. I would assume that the Kanzlei des Führers would be turned into the President's staff.
In the end it was all moot of course, but "Party Minister" is basically just giving "the head of the Party Chancellery" a proper title.