Is it even possible to challenge the character? Or does the phrase really mean "challenge the player's ability to build a character, and then use those abilities"?
Another way to phrase your second paragraph would be to challenge the player through the character.
If, for example, the challenge is a riddle or a puzzle that the player or players solve without the skills and abilities of their character(s) then you are challenging the player directly, the character used is irrelevant.
If, on the other hand, the challenge presented requires the players to use the skills/abilities possessed by their characters and cannot be conquered, solved, without the use of those skills then you are challenging the players through their characters.
Just a thought.
Like a great mzny things it has meaning in contrast and context to other things.
A truly virtuous character knows that it is never disadvantageous to do the right thing!"A challenge of character" would be a role playing challenge. For example putting the character is a moral dilemma where the player has to decide if the character will stick closely to their professed alignment even when it might be disadvantageous to do so.
[MENTION=50987]CleverNickName[/MENTION] and [MENTION=6919838]5ekyu[/MENTION] and [MENTION=762]Mort[/MENTION] get it. As was said, meaning is rarely in a vacuum. Challenge the character is simply shorthand for setting a challenge in the game that is addressed to the fictional abilities of the character and not directly addressed to the player.
Is it a challenge to the player or to the character, and why?
But does that actually "challenge" anything? It seems to me the character, which in this case means the numbers associated with the character, are just a constraint on the player's actions. But the player is still facing the challenge.
Two players both wish to accomplish the same thing in the same way, but one player adds 6 to the roll of a d20, and other subtracts 1 from the same roll. The first player has a higher chance of succeeding, obviously. But what or who has been challenged, and how?
The only challenge I see being addressed is that the first player in some sense "anticipated" this sort of challenge by making those particular choices for his character build.