Centigrade, Celsius and Kelvin
All three of these are acceptable metric units for measuring temperature, but the first of these to come into existence was centigrade. It was measured as a scale from 0C the melting point of water, to 100C the boiling point of water. Later we switched to using the triple point of purified water as 0C which was very slightly higher. It had been discovered that the temperature at which water melted could vary with pressure, but the triple point, that temperature and pressure at which water can exist as solid, liquid or gas, was more fixed. The purified water clause stated the make up of the water to standardise the definition so that it could be taken to a higher degree of accuracy.
Before this switch had happened a need came along to pay attention to absolute zero: the lowest possible temperature. This was set at being 0K, but with the same size steps as centigrade. Thus 0K was equivalent to -273.15C. However you can't just add a nice-ish number like that and expect to have all three points (absolute zero, melting point and boiling point) match up with rational numbers. This scale gave a melting point of 273.1499K. Because we care about making absolute zero precise more than we care about the melting point of water, water actually melts at -0.0001C. There's a pedantic sort of fact if ever I saw one.
For the record, the triple point in centigrade and Kelvin are 273.16K and 0.01C, where both of these numbers are precise by definition.
Confused? Yeah, I am a bit as well. The people devising the system had so many numbers which almost worked that they just had to bodge it.
The Celsuis scale is the name of the centigrade scale from 1948 onwards. It was named after Anders Celsuis: the invented the centigrade scale in the 18th century. Since all the bodging with absolute zero and triple/melting points had happened before this name change Celsuis has only had one definition for its existance: while centigrade can refer to any of a collection of related historical scales. The old name was disposed of because France and Spain were still using Grades instead of Degrees to measure angles for some things. There are 100 Grades in a right angle and so they were called centigrades. This led to confusion and so the international community switched to using Celsuis. Both are still correct, but centigrade is becoming more more archaic. In 1985 the BBC finally switched over to using the term Celsuis for their forecast, but you can use whichever you like.
