You may be correct. I think it's fair to say Grant was one of the first American commanders to use overwhelming force on offense to finish off an opponent.
Both Lee and Grant served under Winfield Scott who used an early form of overwhelming force in the Mexican War. Lee tried to use a similar tactic in the two northern invasions and failed, partly due to inadequate supply lines. Grant was able to use overwhelming force because he had the resources and he knew the south didn't. I've always felt that the generous terms Grant gave Lee at Appomattox was a gesture of respect, Grant knew that it wouldn't have been a fair battle and he also knew that in a "fair" fight the "safe money" would have been on Lee.
You're right. Grant believed that winnning meant crushing the enemy. Still the best strategy.