To make it easy to compare the terms for all forms of ice-containing precipitation used by US weather scientists, I have pulled together the following comprehensive list of such terms from the meteorological glossary of weather.com. (Strangely, the 'wintry mix' that others have also mentioned in their responses doesn't appear in this glossary, even though I have often heard it from the lips of US weather forecasters — including those of the Weather Channel.)
Note that this list accordingly has a bias towards US usages. As others have remarked in their answers here, some of the terms, such as sleet, are applied differently in Britain; unfortunately, there doesn't currently seem to be a corresponding list on the website of the UK's Meteorological Office. (If there is, I could not find it.)
Precipitation that is liquid, but freezes upon impact with a solid surface, such as the ground or other exposed surfaces.
Rain that falls as liquid and freezes upon impact to form a coating of glaze on the colder ground or other exposed surfaces.
The covering of ice crystals that forms by direct sublimation on exposed surfaces whose temperature is below freezing.
A form of frozen precipitation consisting of snowflakes or ice crystals and supercooled water droplets frozen together.
Precipitation that originates in convective clouds, such as cumulonimbus, in the form of balls or irregular pieces of ice, which comes in different shapes and sizes. Hail is considered to have a diameter of 5 millimeter or more; smaller bits of ice are classified as ice pellets, snow pellets, or graupel. Individual lumps are called hailstones
Another name for frost. A deposit of hoarfrost occurs when air with a dew point below freezing is brought to saturation by cooling.
Precipitation in the form of slowly falling, singular or unbranched ice needles, columns, or plates. They make up cirriform clouds, frost, and ice fog. Also, they produce optical phenomena such as halos, coronas, and sun pillars. May be called "diamond dust."
Precipitation in the form of transparent or translucent pellets of ice, which are round or irregular in shape. They have a diameter of 0.2 inches (5 mm) or less. They are classified into two types: hard grains of ice consisting of frozen rain drops or largely melted and refrozen snowflakes; pellets of snow encased in a thin layer of ice which have formed from the freezing of droplets intercepted by pellets or water resulting from the partial melting of pellets.
A severe weather condition characterized by falling freezing precipitation. Such a storm forms a glaze on objects, creating hazardous travel conditions and utility problems.
The rapid freezing of supercooled water droplets as they touch an exposed object, forming a white opaque granular deposit of ice. It is one of the results of an ice storm, and when formed on aircraft it is called rime icing.
Also known as ice pellets, it is winter precipitation in the form of small bits or pellets of ice that rebound after striking the ground or any other hard surface.
Snow or ice on the ground that has been reduced to a softy watery mixture by rain and/or warm temperatures.
Frozen precipitation in the form of white or translucent ice crystals in complex branched hexagonal form. It most often falls from stratiform clouds, but can fall as snow showers from cumuliform ones. It usually appears clustered into snowflakes.
Frozen precipitation in the form of very small, white, opaque grains of ice. The solid equivalent of drizzle.
Frozen precipitation in the form of white, round or conical opaque grains of ice. Their diameter ranges from 0.08 to 0.2 inch (2 to 5 mm). They are easily crushed and generally break up after rebounding from a hard surface, unlike hail. Sometimes it is called small or soft hail.
A wintertime thunderstorm from which falls snow instead of rain. Violent updrafts and at or below freezing temperatures throughout the atmosphere, from surface to high aloft, discourage the melting of snow and ice into rain. Intense snowfall rates often occur during these situations.