The Police Story series can be quite confusing (especially to a newbie of the series), since the titles are different in all various countries. Here, I will try to help you understand each installation with caps, info and my review of each film.
Police Story II
Police Story III: Supercop
Don't get confused with Michelle Yeoh's Supercop (Supercop II). Jackie's character only places a cameo, but in the actual Supercop he plays along side Michelle Yeoh.
Police Story IV: First Strike a.k.a. Jackie Chan's First Strike
The first Police Story to be filmed in English.
Police Story V a.k.a. New Police Story
As the title says, this is a whole new police story with new characters, although still Jackie Chan playing the lead.