A snow crystal, as the name implies, is a single crystal of ice. A snowflake is a more general term; it can mean an individual snow crystal, or a few snow crystals stuck together, or large agglomerations of snow crystals that form small balls that float down from the clouds.
Snowflakes are not frozen raindrops. Sometimes raindrops do freeze as they fall, but this is called sleet. Sleet particles don't have any of the elaborate and symmetrical patterning found in snow crystals. Snow crystals form when water vapor condenses directly into ice, which happens in the clouds. The patterns emerge as the crystals grow.
The term snowflake has also been used a slur against childish millennials. It is defined as someone who believes they are as unique and special as a snowflake (which occurs when they are told so by indulgent liberal parents), as well as someone who is hypersensitive to insult or offense, especially a young person on the Left who embraces political correctness and the sensibilities connected to it.