The center game goes 1:e4 e5 2: d4.
The Scotch game is 1: e4 e5 2: Nf3 Nc6 3: d4
The Scotch variation is 1: e4 e5 2:Nf3 Nc6 3: Nc3 Nf6 4: d4
All of these same to be attempts at taking central superiority. As far as I can tell the only difference is in how much they may possibly restrict their opponents choices (the knights block in several pawns) and also the amount of pieces ready to take the center or defend it when it breaks.
What are the main advantages and disadvantages of each of these and what's stopping me from playing the Center Game so that my opponent has no chances to branch away from the 2 knights and 4 knights games?