Man vs ManMontresor wanted revenge for Fortunato because he was insulted by him (Fortunato) once. This is an external conflict between two characters.
Man vs SelfWhen Montresor noticed that Fortunato finally died, he felt guilty about it. According to the story, Montresor's "heart felt sick". This is an internal conflict because Montresor felt bad about his own action (which was murder).
Verbal IronyBoth characters said the same lines : let us be gone. Montresor meant that as dying, and Fortunato meant that as going back upstairs.