What's the difference between a theme and motif?
A theme is a big-picture idea, and a motif is a recurring symbol.
Most stories can be reduced to a single theme, an overarching idea, that every element of the story will support and bear out. "Violence begets more violence," "crime does not pay," "we are only as good as the way we treat the helpless and vulnerable," "there's no such thing as a free ride," "good intentions don't redeem bad deeds," etc. Two different readers might not agree on what the story's most important theme is (most stories have more than one), but there's always some big idea to latch onto.
A motif is a recurring symbol that serves as an omen for the characters and the reader. In the films of John Woo, a white dove flies through the scene to symbolize the presence--impending or otherwise--of death. In Dr. Who , we see a fracture in walls, windows, the air and time itself as a reminder that messing around with primal forces has consequences, and those consequences are coming.
It's a Wonderful Life has examples of both. Its theme is "one good man can make a huge difference in the world" and its recurring motifs include flower petals, the record player, and immersion in water as turning points for the protagonist.