What is the difference between a symbol and a motif?

A symbol is often an object that is described in a text which has a deeper meaning than what it may seem at surface level. It appears singularly or few times throughout a novel or play, for example, flying birds may indicate a character being 'free' whilst a caged bird could elude to a sense of entrapment. A motif appears frequently and constantly through a given text- implying an overall message of the novel or play. For example, the writer may consistently refer to the use of light or lack thereof, to exaggerate an uncovering/ hiding of a character's actions. A symbol often only relates to a certain character or part of a text, whereas a motif helps explain an overall theme of the entire piece.