Why is there a 50-move rule and a 75-move rule? Logically, if 75 moves have been played, 50 moves would've also been played. This sounds ridiculous. It is like saying &quot;I would buy this book if it cost under $60 and it costs under $40&quot;. So, what is the logic behind that?
From the FIDE Laws of Chess:

50-move rule:


  9.3 The game is drawn, upon a correct claim by a player having the move, if: 
  (...) 
  the last 50 moves by each player have been completed without the movement of any pawn and without any capture.


75-move rule:


  9.6 If one or both of the following occur(s) then the game is drawn: (...) any series of at least 75 moves have been made by each player without the movement of any pawn and without any capture.


(emphasis mine)

As you can see, the decisive difference is that the 50-move rule only applies if a player correctly claims it, while the 75-move rule applies independently of any claims. So, in the 50 to 75 move window, the players can claim for a draw, but don't have to (and play on). Only when the 75th move without pawn moves or captures has been reached, the arbiter may interfere and declare the game drawn.