The basics:

• A match is either Rimfire or Centrefire.
• You must shoot with one hand only
• 10 shots are fired at each target in two strings of 5 shots each.
• The X, inside the 10 ring, is the highest shot possible. 
• A perfect target, with a score of 100 (10 shots in the 10 ring), is called a possible
• Matches have stages, each with a distinct course of fire.
• There is the Slow Fire stage, Timed Fire Stage and the Rapid Fire stage

Two similar rule systems (ISSF & CMP - formally ISU & NRA) have co-existed since the late 1800's.

The premise is the same and the same core pistol target shooting skills are required

25M Pistol

25M Center-Fire Pistol

25M Standard Pistol

• Set times for preparation time and load command.
• No pre-charged magazines are allowed (you many only load after the "load command" is given.)
• Turning targets are used for the Sport Pistol (25M Pistol) and Centerfire Pistol - Rapid stage
• Electronic Targets are required for High Performance matches
• Centerfire shots are scored as .38 caliber
• The grip can't touch the wrist.
• 
  

CMP Precision Pistol was the inspiration for the ISSF pistol events. As such, the events and match conditions are similar but the rules differ slightly as does the match format (the course of fire).

• A special handicap classification system is utilized
• The distances are in yards (25 yds / 50 yds)
• The size of the scoring rings are different
• Optical sights are allowed
• There are no turning targets
• The commands are worded differently
• RO decides when the line is ready
• The rules for allowable malfunctions are different
• For centerfire, the size of the caliber is irrelevant
• Special grips (allowing more support) are allowed
• You are allowed to pre-load magazines
• 
  

Pistol Bullseye shooting can refer to several disciplines (see Wiki).

Small-caliber pistol (.22 LR)

• ISSF 25 M pistol
• ISSF 25 M standard pistol
• ISSF 25 M rapid fire pistol
• ISSF 50 M pistol
• CMP Precision Pistol

Large-caliber pistol

• ISSF 25 Meter (center-fire) pistol encompasses many centerfire cartridges, but the dominant caliber is the .32 S&W Long.
• CMP Precision Pistol centerfire matches require pistols of calibers between 32-45. Typical cartridges include. 32 ACP, .32 S&W Long,  .38 Special, 9×19mm Parabellum, and .45 ACP.

• Although some of the bullseye disciplines are not in the Olympics, the SFC depends on these disciplines (and other highly competitive and enjoyable shooting sports) to identify talent and help create pathways for athletes to become Olympians and long-term sport participants.

• Athletes gain match experience first at club level matches, regional matches, provincial level matches and then at the National Championships before moving on to international competition. The pathway is similar for Pistol Coaches and Pistol Officials as they advance their qualifications..

• Certain calibers are not effective at 50 yards. Example even though the  .32 S&W Long is preferred at 25 M and 25 yards, it is the .32 ACP that is used for the CMP matches since the slow fire stage it shot at 50 yards where the .32 ACP is far superior.