A pulley is replaced because the grooves are worn or because the drive ratio changes. In the first case, the reference stays the same. In the second, changing the diameter alters the machine speed, the belt length and the load on the bearings; it is worth reviewing both pulleys and the centre distance before deciding.
Also check that the pulley profile and the belt profile are the same. A belt of similar section may enter the groove and seat badly. In toothed pulleys, pitch and tooth profile must match those of the belt exactly. The taper bushing is chosen by the size the pulley calls for and by the shaft diameter.