The first difference is that Kerosense will not gel under very cold temps as fuel oil will gel at very cold temps. This is why you see in outdoor tanks for those who heat with oil they use kerosene.
Kerosense is readily available in the northeast at gas stations to buy on a self service basis. The only place to get a product similar to heating oil would be to buy diesel fuel but that has taxes on it and heating oil in most parts of the country doesnt contain any taxes. Heating oil is dyed red, kerosense sold at a retail pump will be clear as the dye causes problems with wicks and some heaters, but the purpose of the dye vs the clear is the indication that the tax has been paid on the clear vs no tax on red.
Also, kerosene and diesel fuel now are ultra low sulphur content in which there is less than 15ppm but heating oil has 500ppm or more.
Im sure there is more chemistry differences but these are the ones I can tell you about.
kerosine will likely burn cleaner than diesel, even if you run ULSD. The hydrocarbons are smaller on average, and sulfur is lower. Clean K1 kero may have fewer aromatics as well, which can also effect soot.
Kerosene burns cleaner, but has a bit lower BTU rating than Fuel Oil, which is basically the same as Diesel. Just use pump diesel and you will get more heat for your money. That is, if the heater's exhaust is vented outside. If not, use Kero.