The first part of this confusion originated in the eighteenth century, when two men, Anders Celsius and Daniel Fahrenheit, both developed thermometers with different scales. Theirs were not the first, however. Galileo is usually credited with inventing the first thermometer, in 1592, but he did not develop a memorable scale to go with it. In the seventeenth century, liquid thermometers were developed and could be made quite accurately, but no standard scale had come into use. In the 1660s, Robert Hooke developed a thermometer scale that went from -7 to 13, and many other scientists also developed temperature scales.
Anders Celsius was a Swedish astronomer. As a professor at the University of Uppsala, starting in 1730, he spent a lot of time making measurements. In 1730 he published a paper on a new method of determining the distance of the earth from the sun, and in 1736 he participating in an expedition to Lapland to measure the arc of a meridian. In conjunction with another expedition to Peru, this measurment confirmed Newton's theory that the earth bulges slightly in the middle. He also measured the brightness of stars by seeing how many layers of a thin film it took before the light disappeared. With the strength of these measurements behind him, he persuaded the University of Uppsala to let him build an observatory, which was completed in 1741. This was the same observatory that Anders Ångström would be in charge of over a hundred years later.
None of those measurements would seem to necessitate having a thermometer, however, and this is in part because his job description as astronomer is different from what we think of today. Certainly measuring the distance of the earth from the sun falls under astronomy, but back in the eighteenth century, so did measuring distances like the arc of a meridian, the changes in the height of seawater, and more meteorological measurements, including temperature. Celsius developed his scale by setting the boiling point of water at 0 and the freezing point of water at 100. He called the units "centigrade", because the distance between those points is divided into one hundred equal steps. This was not radical, as that was the way most scales were created--by choosing two points and putting a certain number of degrees between them. Celsius took his study of temperature one step further. He was not content with just making a thermometer that worked in Uppsala, but wanted to better understand the nature of temperature and make sure that it was independent of location. By making measurement in many places, along with measuring the atmospheric pressure, he determined that the freezing point, but not the boiling point, was independent of pressure, though neither depends on latitude. He published a paper reporting his results entitled "Observations on two persistent degrees on a thermometer" in 1742. He died only two years later of tuberculosis.
If you were paying attention when I mentioned what the two points of his scale were, you will notice that his scale went backwards from what it does today--the boiling point of water is 0 and the freezing point is 100. The switched scale, as we know it today, was made popular by Carl Linnaeus, the Swedish botanist famous for originating the biological nomenclature used today. He made measurements of the conditions in which plants grow, and for him, the freezing point of water was vital, since many plants die below that temperature. In a paper published in 1745, only a year after Celsius's death, he used the same size of a degree and the same fixed points as Celsius, but placed 0 at the freezing point of water and 100 at the boiling point. The modern Celsius scale was born. Well, not quite.
Celsius had called his scale the centigrade scale, and it continued to be called that for centuries. It was not until 1948 that the Ninth General Conference of Weights and Measures renamed degrees centigrade degrees Celsius, and caused even more confusion. So the next time someone says "degrees centigrade," they aren't wrong, per se, just outdated.
Sources and further information:
Temperature Scales from the early days of thermometry to the 21 st century
History of the Celsius Temperature Scale