Challenge is the overall difficulty of obstacles to overcome by player, but accomplishment is the level of reward that is gained.
Similar to effort/reward metric, games which provide little of an accomplishment for overcoming a challenge will be perceived as hardcore or ignorant of players accomplishment - psychologically the "accomplishment" is all within their heads vs game accomplishment actualized in in-game rewards.

Challenges that are unfair by themselves(i.e. giving the enemy too much advantage vs player) change quality of experience - games which employ such challenges break the unspoken "fairness" expectations.Accomplishment of such unfair challenges creates pride in overcoming "game against all odds" where player is outmatched but somehow succeeds.

The goal of optimal design is to trick the player that he is "accomplishing" grand challenges without appearing too unfair(rigged game) or too easy(rewards disproportionate with effort).