That's irrelevant. It doesn't matter that they are the same reward - it is sufficient to note that the player *does* get something out of it.
If you think the person does get something out of it, fine - let's discuss what they get out of it, not what we might imagine that an imaginary character might get out of it, if they were real.
No, the form is important. Players frequently form attachments to their PCs - rewarding the PC makes use of the emotional attachment. You can ignore that connection, but you're discarding a strong and useful tool in so doing.
Yes, the player may well form an attachment with the character, but if we are to make a good judgement of whether the "reward" is useful for our game objectives, we should consider the value of the reward to the player, not to the character. In other words, a reward is "useful" or "not useful" based on its value to the player, not on its value to the character.
In addition, rewarding the player through the character helps makes sure the character action and player actions are aligned. If you reward the player through a method that isn't directly connected to the character, you risk unintended consequences.
Now, there's a hole with no bottom. If you want to talk "unintended consequences" let's talk about how the "reward" is justified and by whom. I honestly think that, if we are getting into someone
consciously deciding upon rewards for players/characters then the nature of that reward is relatively small beer, as far as "unintended consequences" are concerned.
No, because that reward is not *meaningful*. Rewards that have no impact are like a stilted pat-on-the-back. Give them something that means something to the function of the character, they'll recognize the value.
The player might superficially see any sort of "power up" as a good thing, sure. But let's pause and consider a minute; a character power up means either:
a) That challenges and opposition will get harder to compensate, in which case this was a reward how?
b) That the mission/task/quest to be achieved will be easier and quicker to achieve, removing both challenge and time spent "enjoying the journey" - again, not a great "reward".
or c) That the power-up has little relevance to the particular challenges to be overcome, which also doesn't sound like much of a "reward".
In the end, although I can see that being "awarded" magic items might provide a momentary frisson for some players, I can't really see them as useful rewards in the overall structure of the game design.