Celsius (or degrees Celsius) is a scale to measure temperature and is derived from an SI unit with the symbol °C.
Celsius is named after Anders Celsius and is a scale derived directly from the Kelvin scale and was established in 1742. Otherwise known as the centigrade scale, it is recognised and used worldwide.
The Celsius scale is exactly 273.15 below the Kelvin scale which is the SI unit for temperature.
Water melts just below 0 °C and boils just below 100 °C (assuming normal conditions). The Celsius scale is also commonly used to measure the weather (or atmospheric temperature) and body temperature to diagnose fever. A typical comfortable day is anywhere from 10 °C - 30 °C and a healthy body temperature is anywhere between 36.1 °C and 37.2 °C.
Degrees Celcius is measured using a thermometre.
Farenheit (or degrees Farenheit) is a scale to measure temperature and is part of the imperial / US customary unit system with the symbol °F.
The Farenheit scale was proposed in 1724 by Daniel Gabriel Farenheit and was the first standardized temperature scale to be widely used.
0 °F was set as the freezing point of a solution made from equal parts ice, water and salt. It was then established that the melting point of ice was 32 °F and human body temperature was 96 °F (or 98.6 °F when the scale was redefined into the modern version of the scale).
It is still used in the US and some associated territories as the official temperature scale. Everywhere else in the world uses Celsius.