The "commercial" designations are collector creations and confusing for sure.
More recent designations are below, simplified and not subscribed to by all, as one still sees
1920 and 1923 used.
None of these are strictly 7,65mm or 9mm as each caliber exists in each category:
-old model parabellum, the "1900" models with leaf spring, and long chamber
-new model parabellum, the "1906" models with coil spring, found with short chamber and a few
with long chamber, some of these may be former "1920 commercials"
Most of the two above would have been commercial pistols, but many were sold under contract
to foreign military entities
-P 04- the navy models-these are 9mm unless modified into "navy commercial"
-P 08 - commercial or military
-L P 08- the lange pistol or artillery model, originally 9mm; unless converted to "commercial
artillery"
-P 14 - a P 08 with grip safety
Alphabet commercial- a P 08 with 1-4 digit serial number with letter suffix
Confusing enough yet?
And I've the feeling I left one or two out, but someone will be along shortly to correct and/or dispute what I have written.
Dwight Gruber is working on a Commercial Luger book, he cannot finish it soon enough for me!