Much more than anyone cares to know...stolen from various on-line sites:

..."The term paraffin oil is used in Britain, New Zeeland, Australia, and some other countries for the same fuel as is known as kerosene in the U.S. and Canada. There are two grades of kerosene: 1-K and 2-K. The former grade is low-sulfur kerosene, with a maximum sulfur content of 0.04 percent by weight, and the latter can contain up to 0.30 percent sulfur. The sulfur content is important because the sulfur in the fuel forms some pretty nasty pollutants when the fuel is burned. Keeping the sulfur content as low as it is in 1-K kerosene allows the fuel to be burned without a flue to remove the exhaust products from the room (such as in a kerosene space heater). 2-K kerosene must be burned only in appliances with a flue. Other than sulfur content, the two grades of kerosene have identical properties.

Lamp oil has been further processed and refined so that it doesn't produce as much harmful smoke, soot and other pollutants. Manufacturers, under pressure from eager consumers, decided to distill kerosene further so the fuel could be burned indoors without as much inconvenience. Now you can find "ultrapure" or "ultraclean" lamp oil at many outdoor suppliers and camping stores."

We've experienced no discomfort using 1-K (K-1) in lamps and in a heater in our cabin. HOWEVER, our cabin has been anything but air tight since Gilbert ventilated it that day with his H&K MP-5. (We don't let him play with us anymore!)