To clarify what the words mean we therefore have to look at all the evidence in the rules, and see how the designers put it into practice. The description is nearly the same in both editions, but in the first edition it's used not only to "magically" turn a failure into a success, but also to fuel some blatantly magical abilities. Which doesn't really mesh with the idea that 'Hope' is just your own inner strength. And even in 2e it's used to power the new "Magical success" mechanic. How is that explained, if the designers were intentionally downgrading Hope to mundane positivity in 2e?
I actually don't see any contradiction in this. Hope is your inner strength, which for most heroes has the mundane effect of making them more likely to succeed ("I really believe I can do this"). If you possess a magic item or an inherent magical talent, then you can channel that very same inner strength into more blatantly magical result (they "unlock" your spirit's potential: the Fëa, or the Ainur's music, whatever you want to call it). This is true for both editions, they simply do the same thing in two different ways.
Personally I see a lot of consistency in the new Hope system, and in how it has been almost seamlessly embroidered with the Inspiration rules, Distinctive Feature usage and the new Shadow mechanics; and I must admit that I struggle to understand the whole "designers must explain their choices" approach of certain discussions, especially when there is no evident flaw in the mechanics (ex. the math is off, no-brainer choices, unclear wording, etc.) unlike in other areas of the game. I can understand that there may be divergent "creative" opinions about almost every authorial choice, but saying that a rule has a problem simply because it doesn't match one's vision is quite a different approach.
Still, it's absolutely worth being debated, because the ideas emerging from such discussions are always precious (for the authors as well). For instance, my only concern about Hope at this point is that its recovery is still a bit too slow for it to work properly, but Francesco has already given encouraging signs on the matter (hence, always remember the mantra: trust Francesco ).
(And I hope that this better explains and settles my previous argument, which I acknowledge was put too bluntly; I didn't want to shut down any discussion, but simply say that theorycrafting may be interesting - and man, do I love theorycrafting - but actual play is where the real truth about a game usually is)