These words refer to something that has existed or gone before. Trace, the more widely used, is derived from Latin tractus, meaning "a dragging." It applies to any evidence, such as a footprint, a fragment, or a lingering odor that suggests the prior existence or presence of something: "There was a trace of perfume in the room." "There was no trace of their having spent the night here." Vestige, a more limited word, refers to some slight but actual indication (remains) of something that no longer exists: "In his weakened condition, he is a mere vestige of his former self." "Not a vestige of her once-great beauty remains." Related words include track, trail, spoor, record, indication, and sign.
Dictionary of problem words and expressions. Harry Shaw. 1975.