Motif
In short: A recognisable element that can recur across stories.
Term
How does it work in the tale?
A shoe that fits can reveal someone’s identity. The material and setting can change while the act of recognition remains recognisable.
How can motifs work differently across tales?
In Cinderella the shoe reveals the identity of the person being sought. In Snow White the apple is a trap set by the disguised queen. To study an object as a motif, note when it appears, whose hands it passes through and what scene it sets in motion. This helps distinguish similar objects from similar narrative roles.