Leitmotif

A short melody is a motif when it can be recognized and developed. In a story, repeated association gives it another job: it points to a person, object, place or idea. One appearance is not enough to establish that connection; the listener learns it through context and return.

Yes. The contour, rhythm, interval pattern or timbre can survive while other features change. A brisk three-note figure may return slowly under a different harmony when the character's situation changes. Listen for the preserved feature, then ask what the changed feature tells you.

Wagner's music dramas are central to the history of the term, but associated recurring themes appear in later theater, film and games as well. Avoid labeling every repeated hook a leitmotif: a repeated idea needs a meaningful dramatic association, not just frequency.

An ostinato repeats persistently as part of the musical texture. A leitmotif may disappear for a long stretch and return at a revealing moment. It can be varied extensively while still carrying the same association.