Different rules are due to the different organizations that run the tournaments.
The USGA runs the Open, so they make the rules.
Before 1926, the golfer played 36 holes on 2 days.
In 1927, they played 18, 18 then 36 on day three.
then in 1965, they started playing 18 over 4 days.
The 18 hole playoff has always been the practice.
Personally, I like the British Open playoff ..4 holes aggregrate score.