The movie series are about the adventures of inspector Chan Ka-Kui.
Project S is a spinoff of Police Story 3 and has only a cameo of Jackie Chan as inspector Chan Ka-Kui.
The exceptions are the last two movies as those are reboots and use another two different roles (New Police Story: Senior Inspector Chan Kwok-Wing, Police Story 2013: Detective Zhong Wen).
I put those in the list because if we don't cling to the names we can treat them as adventures of the old inspector..