Pawn Push

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A Pawn Push is a quiet, irreversible move of a pawn one single step forward, or optionally but only from its initial rank, two steps forward. The condition for a pseudo-legal pawn push is that its target square ahead, the stop square, is empty, while the origin square is obviously occupied by the pawn of the side to move.

Double Push

The double pawn push from the initial rank requires both squares ahead empty. Making a double push is a precondition to set the en passant target square in the obtained position, as specified by initial Forsyth-Edwards Notation (FEN) unconditionally, where todays programs are instructed to set en passant target square if the en passant would be pseudo-legal (an opponent pawn left or right) or even better strictly legal [1], also considering updating Zobist keys during make move to avoid dissimilarity of otherwise repeated positions if the first occurrence happened after a double pawn push with no en passant capture actually possible [2].