The terms "motif" and "motive" mean very different things in English although they both derive from the Latin verb "movere" (to move).
Motif comes into English via French and means a theme or recurring idea in a literary work. It is normally an idea which recurs and has some sort of symbolic significance for the story. In music, a motif is a recurring musical idea or melodic fragment.
Motive arrives in English via the late Latin "motivus" and means motivation or something that impels one to act a certain way. In analysing plot in narratives, one often analyses what motives caused characters to act a certain way.
Although motif and motive sound the same, their meanings are very different from each other, and so, care should be taken when writing essays - not to confuse one spelling when meaning the other.
Just to add to the above post. Here are some examples of motif and motive:
Darkness is a motif or recurring symbol in Macbeth, (among many other motifs like manipulation and blood) because it is often used to infer the gloomy setting and imagery and suggestion of evil. For example, Banquo in Act 1 Scene 3 mentions "The instruments of darkness tell us truth," - Here Banquo comments after encountering the witches, and describes them using the motif darkness to link to their evil and wicked nature.
Police forces are inquiring into the motive behind the murder.
Some speculate whether Othello's motive for killing Desdemona was out of honor or jealousy.
- The use of motif and motive are used frequently within literature. Analysing characters often entail deciphering their motives (reasons) behind an action, and motifs are often found when analysing the book, play or novel or poem as a whole to identify any recurring themes or symbols.