They are not entirely different. The resolution refers to that point when the conflict within the story is resolved. This happens in stages in "The Cask of Amontillado." The main conflict involves the insult Montressor feels he has endured from Fortunato. This conflict is resolved(for the most) when we realize Montressor's plan for revenge and the details of how it will be accomplished, i.e. chaining him to the wall and beginning to brick him in. The outcome of the story is the death of Fortunato, which never occurs in the story and we can only infer as readers. This would explain how they are different. One occurs within the story, the other does not.
The terms 'outcome' and 'resolution' refer to the ending of the story--how Montresor achieves his aim in taking his revenge by burying alive Fortunato. Montresor has meticulously planned the time, the place and the method of his revenge well in advance.
1.Time: Montresor decides to take his revenge at "about dusk, one evening during the supreme madness of the carnival season," so that every one in his house especially the servants would have gone out and that he would be able to commit his heinous deed completely unnoticed by anyone. He had cunningly ensured that the servants would not return home that evening by lying to them that he will be returning home only next morning.
2.Place: Montresor chose the innermost crypt in his vaults so that Fortunato's cries would not be heard by anyone. He had also arranged to have the building stones and the mortar ready at hand to wall in Fortunato. When he accompanies Fortunato into the vaults he carries with him the instrument of revenge-the trowel.
3.The Method: All the while "smiling in his face" Montresor flatters and traps Fortunato by exploiting his "weak point" : Fortunato "prided himself on his connoisseurship in wine," and Montresor deceives him by saying that he does not wish to trouble him and that he'd rather seek Luchresi's opinion regarding the quality of the Amontillado that he has bought. At once Fortunato takes the bait and accompanies Montresor into the vaults to prove that he is better than Luchresi. Once inside the vaults, Montresor gets him drunk to slow down his reflexes and then leads him to his death.