There is a very fine line sometimes between Snow, Sleet (a.k.a. Ice Pellets) freezing rain, and plain old rain.
First of all... all start out as a solid. If the solid precipitation falls to the ground through an entire layer of sub-freezing temperatures (or a very shallow layer of warm air only at the surface)... then it falls as snow.
If that solid precipitation falls through a deep enough warm layer at the surface... it will have melted enough to fall as plain old rain.
For freezing rain... The layer near the surface is below freezing and there is a shallow warm layer above it... The snow melts completely as it falls through the warm layer. The warm layer has to be shallow enough for the now liquid precipitation to be "supercooled" (in liquid state but just slightly below freezing). When it falls back through the very shallow freezing layer at the surface, it immediately freezes to any surface that is below freezing.
For Sleet (a.k.a. Ice Pellets), the process is nearly identical to freezing rain. The difference is the freezing layer close to the ground is deeper and the warm air above it is shallower. This causes the snow that falls through it to only partially melt. The precipitation then falls through the thicker layer of sub-freezing air near the surface, and re-freezes into a ball of ice before hitting the ground.