I think people are going to have different answers here, and that this is more of an ongoing conversation in each style within the hobby. Ultimately I find, when I talk with Estar, a lot of what he says about fairness resonates. But there is a lot here.
For me, first and foremost is fair application of the rules. I shouldn't give apply the rules differently to Steve than I do to John. And I think I would add to that, you should apply the rules fairly to the monsters and the NPCs too (this may just be my own take, I can't say I am speaking for others on this one). To me that is important because that gets at the fairness of the players expectations of things like strategic choices, tactics, etc. I think fairness also extends to what the players try to do: if a player wants to start a cult to a new deity of coffee, and has some methods for persuading people to follow, the GM ought to hear those out and try to adjudicate that scenario as fairly to the player as possible (and unfair adjudication here would be something like, the GM simply not wanting to deal with a coffee cult at the moment, so he makes it never materialize or barely materialize). A fair GM will take that goal seriously. Now maybe starting a coffee cult in that setting, at that moment, with the players present resources, is a bit boneheaded and won't work. But I think a fair GM will also give the player a sense why such efforts are not working, so it is clear it isn't just an arbitrary decision. Fairness is giving players the win, even when it is inconvenient to the campaign, the adventure, what the GM wants, if the players legitimate get a win. Fairness is also how you treat people at the table, and I do think that can extend to situations like having a player who simply isn't good at one aspect of play but wants to engage it (here is where I usually give people an A for effort, or I rely on things like Skill rolls to help balance that stuff our). I do think this one is a delicate situation because if you shift something like that for a player who is having a hard time, a player who isn't may feel like they are having to work harder for their success. But just as an example, Elliot in both those games is one of the most eloquent players in the group, and a great actor when it comes to playing his character. I am not, but I can string sentences together and make a compelling case for things. If I were a GM handing me and elliot in the same situation, I would focus more on what I (the player in the example) is saying, and more on Elliot's performance probably to get a sense of how convincing each one is being (because obviously there is a massive disparity in acting talent there). So I think as long as the player is bringing something to the table, in those cases, it is pretty manageable and neither one feels shortchanged.