What is the difference between a snow flake and an ice crystal?

Snowflakes and snow crystals are made of ice, and pretty much nothing more. 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 "puff-balls" that float down from the clouds.

Snow flakes are ice crystals that are hexagonal in shape. Other shapes of ice crystals exist, most common being ice rods, single bar shaped growths of frozen water. Ice crystals are generally solid growths while flakes are feathery and have an open internal structure. Both flakes and crystals can gather into larger assemblies which have their own nomenclature depending on that ultimate structure.

https://en.wikipedia.org/wiki/Snowflake
https://en.wikipedia.org/wiki/Ice_crystals