Well, it is not "just like in original Chess", as in original Chess you can never go back. So there is ambiguity whether to interpret the FIDE rule for Pawn moves as a location-dependent move or as a one-time initial move. In many Chess variants where you can go back (e.g. Crazyhouse, where captured Pawns can be dropped back on 2nd rank) a Pawn that returns there will again be able to move two squares forward. The advantage of that is that you do not need any 'hidden game state', to remember which Pawns have already moved and which not; just looking at the position will tell you everything you have to know. (About the Pawns. Castling rights are of course an example of hidden game state that even occurs in orthodox Chess.)
Well, it is not "just like in original Chess", as in original Chess you can never go back. So there is ambiguity whether to interpret the FIDE rule for Pawn moves as a location-dependent move or as a one-time initial move. In many Chess variants where you can go back (e.g. Crazyhouse, where captured Pawns can be dropped back on 2nd rank) a Pawn that returns there will again be able to move two squares forward. The advantage of that is that you do not need any 'hidden game state', to remember which Pawns have already moved and which not; just looking at the position will tell you everything you have to know. (About the Pawns. Castling rights are of course an example of hidden game state that even occurs in orthodox Chess.)