A swing uses a wide movement arc as the bell travels from the floor between your feet to a position anywhere from waist height to straight overhead with the working arm/arms held straight.
A snatch is executed with the bell kept as close to the body as possible with the finished position at lockout overhead.
Both exercises key on an explosive thrust of the hips to propel the bell upward.
Swings:
Snatches:
(I never use such a pronounced jump as the guy in the video, but whatever floats your boat)