No, it is different. If the DM says no to the wizard, she's negating one of the character's class features. If the DM says no to the fighter, she's not negating one of the character's class features. And while the DM is technically allowed to negate a character's class features, it's a far bigger violation of the game's social contract than not letting a character do something that isn't on their character sheet, so much so that it's generally accepted that it can only be done if the DM has said ahead of time (ideally ahead of the game even starting!) that it's going to happen.