In "The Tell-Tale Heart," the narrator tells the reader the explicit motive for murder. The narrator describes the old man's "Evil Eye." It is like "the eye of a vulture," "a pale blue eye, with a film over it" and it makes the narrator's blood run cold. It is this eye that the narrator says causes him to decide to kill the old man. This explicit motive for murder is again made clear by the narrator's process of planning the murder. He enters the old man's room seven days consecutively, but each time, the old man's eyes stay closed; the narrator is unable to commit the murder when the old man's eyes are closed because it is the evil eye that bothers him.
Implicitly, the narrator's motive for murder appears to be his insanity. The narrator's constant claim that he is not mad comes across as a bit of a "thou doth protest too much" situation. The more adamantly the narrator struggles to prove he is not mad, the more mad he seems. Even the explicit logic behind the murder points to the narrator's insanity; committing murder because the appearance of someone's eye disturbs you is an insane reason to commit murder! The narrator's perceived "over acuteness of the senses" is also a sign of his insanity. He claims to hear "all things in the heaven and in the earth" and "many things in hell," but no one else is able to hear all of these minute sounds. The narrator seems to be imagining these sounds.
Through explicit and implicit details, the reader can easily discern the motive behind murder in "The Tell-Tale Heart," but it is much more difficult to understand the motive for murder in "The Cask of Amontillado." In "The Cask of Amontillado," the reader is introduced to two characters: the narrator Montresor and his friend Fortunato. In the first few lines of the story, Montresor explains that he has suffered "thousands of injuries of Fortunato" and he was able to dismiss all of these, but now Fortunato has insulted him. Although the reader is given this vague explanation as to why Montresor must kill Fortunato, Montresor never explains how Fortunato insulted him.
The reader is made to understand that Montresor's motive for murder is revenge, but is never told what exactly Montresor is avenging. To justify the murder, Fortunato is made to look like a fool and Montresor emphasizes his need for revenge. Fortunato is first described as wearing "motley;" the narrator further explains that Fortunato "had on a tight-fitting parti-striped dress" and he is wearing a jester's hat. He is wearing a fool's costume for the entirety of the story. He is also excessively drunk when he is first introduced to the reader. Despite already being drunk, Fortunato continues to accept more alcohol as he follows Montresor into the catacombs. These details shape the reader's impression of Fortunato as a fool.
Montresor's need for revenge is presented in the first paragraph of the story, but the reader is reminded of it in other places throughout the text as well. Fortunato asks Montresor what his family's motto is and Montresor replies with, "Nemo me impune lacessit." This motto translates to "No one attacks me with impunity." This suggests that a core value for Montresor is revenge; no wrong committed against him will go unpunished. In the opening to the story, Montresor explains that he feels insulted by Fortunato and this insult cannot go unpunished. It is clear that Montresor does not forgive easily, but the reader is never told how serious the insult was.
I think it is easier to understand the murderer's logic in "The Tell-Tale Heart" because insanity needs no reason; the reader doesn't expect an insane person to act reasonably. In "The Cask of Amontillado," the murderer seems sane so it is difficult to understand his motive for murder, especially because he only gives us a vague explanation of being wronged.