Is there any difference between K-1 and Jet A fuel? Yes...well no, well maybe somewhat! According to placards there is a difference, K-1 is 1223 and Jet A is 1863.
According to the MSDS sheets, the flash point for Jet A is 100ºF and the flash point of Kerosene is 100ºF. The Flammability Classification for both is Class II Combustible Liquid. The boiling point for both is between 330 - 550ºF and the specific gravity Jet A is .81 and .83 for Kerosene.
Jet fuel is available with an additive for icing; you won't find that in K-1! Not many outdoor fuel tanks need protection above 15,000 feet! However, I have heard customers say that they don't seem to have the water problem in their storage tanks with Jet A like they do when they use K-1.
You can buy jet fuel undyed, but not dyed. K-1 is available only undyed. According to the state, when K-1 is dyed red, it ceases to be K-1 and it is now Kerosene! For heavens sake! How can that be? Well it's called revenue in the form of taxes.
Jet fuel can only be sold for aviation; it's illegal to sell Jet fuel for on road purposes or heating purposes. The tax for jet fuel is 3 cents per gallon for the state of Michigan and 21.9 cents per gallon for the IRS (unless you are agriculturally exempt and then the Federal Excise Tax is 0).
K-1 cannot be sold into a plane according to the state. If, however a distributor delivers K-1, they are required to charge the 15 cents road tax up front. If the distributor were an ultimate vendor they wouldn't have to charge agriculturally exempt customers the Federal Excise Tax of .219 cents. They can apply back for that from the IRS. Some distributors may not be able to get the tax back, then they would have to collect the tax up front from you. The most unfortunate thing about this scenario is the 15 cents is lost, because you can't get it back from the state.

The bottom line, assuming K-1 and Jet A can be purchased for the same price and it's being used for agricultural purposes, Jet fuel will only have 3 cents in taxes added on and it is legal and K-1 will have at least 15 cents added (non-refundable) and possibly an additional 21.9 cents (refundable) could be added on and it is illegal.
So I'll ask again...is there any difference between K-1 and Jet A fuel? Yes. There definitely is a classification difference, which causes a tax difference, which results in a legality difference.