1. A famous space advantage
2. Space, but no advantage
When one player's most advanced pawn crosses the center of the board to the fifth rank and remains there, they have more space. But for one side to have a space advantage, this expansion should ideally leave no weaknesses for the opponent with less space to exploit.
In position 1 (Capablanca - Treybal, 1929), black can only sit and wait for white to exploit his advantage in space with an eventual b5 pawn break.
In position 2 (Avery - Gligoric, 1971), white has more space but no advantage. Black exploited the combination of white's misplaced pieces and potentially weak dark squares with the exchange sacrifice 21... Rf4!. White was left with no choice but to take the exchange, opening the position for the bishop on g7, as black would simply have captured the advanced and now weak pawn on g5.
See also: "Exchange Sacrifice" "Pawn break/lever"