What is the difference between a symbol and a motif in novels, plays or short stories?
The primary difference is the motif requires repetition and symbols imply representation.
Symbols always stand for something. They are used in a representative way. This means that examples of symbolism will always offer a meaning (even if this meaning is open to interpretation). Of course, it is in the act of reading that objects, events, characters and ideas become symbolic. It is up to you, as the reader, to identify examples of symbolism. Every time you do, you will be making an interpretive claim that "object A" represents "idea A".
Motif is does not require this kind of correlation as motifs are not exclusively representative. If we look at the food references in The Great Gatsby, for example, we see a recurrent motif that is not necessarily symbolic because it doesn't seem to represent a single idea.
Motifs can become symbolic, which is perhaps where you get confused. If this is the case, an object, idea, character or event must be repeated and be representative.