In-game, the D&D character knows about spell slots, but the Fate character doesn't know about Fate points. It is a substantive in-game difference that the D&D character knows about spell slots, and can plan around them.
In-game, Fighters are known for their physical resilience where Thieves are not. This is all in-game stuff. When the characters discuss who to send ahead to brave the poison-gas room, it makes sense in-game to suggest that the Fighter has a better chance of surviving it. Of course, if you have a human Fighter against a dwarf Thief, then it might get fuzzy (just as the math will also get fuzzy, and we can't tell who has a better chance unless we know more details).