In various posts, but particularly in the topic Time plus, the idea is expressed that there is value in saving time by playing quickly in order to gain an advantage on the clock versus our opponent (particularly under Fischer timing where unused increment accrues on the clock versus Bronstein where it does not). This is an interesting idea worthy of its own topic.

The implication is that it is possible to play more quickly than your opponent in the early going in order to build up an advantage on the clock, without incurring an offsetting disadvantage on the board. In other words we would claim that additional thinking in the early going has no value on the board. However, the advantage accumulated on the clock can then be converted to an advantage on the board later in the game by playing slower than your opponent. In other words we would claim that additional thinking later in the game has value on the board. Hmmm... ;-)

Otherwise the implication is that we are not talking about winning "on the board" but rather "in the game", i.e. winning on time. Here again, however, either the opponent has failed to retain enough time on the clock to properly finish up the game while we have, or we have the ability to disrupt the opponent's time management through creative play on the board using our additional time. How this differs from the previous paragraph is not clear to me.