Indeed, 'enhanced' or 'augmented' describe something that is larger, but unchanging. 'Progressive', on the other hand, implies an ever increasing sequence of values. The number of moves of your Pawns is large, but it does not grow during the game. When you say 'Progressive Pawn' I would imagine a piece that gets more moves every time you move it. E.g. a single capture straight ahead on rank 2, a normal Pawn on rank 3, capture to the 3 forward squares on rank 4, capture diagonally forward or sideways on rank 5, etc.
Indeed, 'enhanced' or 'augmented' describe something that is larger, but unchanging. 'Progressive', on the other hand, implies an ever increasing sequence of values. The number of moves of your Pawns is large, but it does not grow during the game. When you say 'Progressive Pawn' I would imagine a piece that gets more moves every time you move it. E.g. a single capture straight ahead on rank 2, a normal Pawn on rank 3, capture to the 3 forward squares on rank 4, capture diagonally forward or sideways on rank 5, etc.