I've found that the best way to determine if I'm using the same colour of white (or any other colour) is to check the label on the ball.

If the label says 'no dye lot' then all balls that you purchase with that colour name will be the same colour.

However, if there is a dye lot on the label, then the only way to ensure that you have exactly the same colour is to make sure that the dye lots match.