In the US “sleet” is the term for a winter precipitation that occurs when snow falls through a layer of warm air and melts into water droplets, then re-freezes into ice pellets as it passes through colder air closer to the ground. In many other areas that were part of the British empire that precipitation is called “ice pellets” and “sleet” instead refers to a mix of snow and rain. In the US that’s called a “wintry mix.”
I would call the frozen raindrop thing hail and the snowy watery thing sleet. I’m from the UK.
Hail is formed through a completely different process and is a spring/summer precip type associated with thunderstorms. It forms as water gets lifted high into the atmosphere from updrafts in the thunderstorm then fall before getting lifted again. Hail often shows layers (like a jawbreaker) and can grow very large.
In the US, sleet/graupel is essentially just a frozen raindrop and is a winter precip type. Wintry mix is what the US National Weather Service uses for any mix of rain, snow, sleet, graupel, and freezing rain. The WMO and Europe use Ice Pellets for frozen raindrops and Sleet for mixed rain and snow. So both are official terms depending on where you are.
