Yes, the only difference between off-road and on-road diesel is the dye added to show that no-tax was paid on the fuel in the tank (of the vehicle that someone may be driving on road).
That being said, on a different note, there are differences in No.2 diesel (most common at diesel pumps...in summer), and No.1 Diesel, and "winter" diesel. Winter diesel may be a blend of No.1 & No.2, or may be No. 2 with additives so it doesn't gel in cold temps, or some combination of all the above.
...and then there's kerosene....which may or may not be No. 1 diesel.
...and home heating fuel oil....which may or may not be the same thing as non-road "diesel fuel" (No.2 or a "winter diesel" depending on what you order and if your furnace tank is located indoor/outdoor.)...This may or may not have the lubricity additives for diesel fuel pumps. May be low sulfur, high sulfur, etc...
I don't understand it as well as others, but I know you can go pretty far down the rabbit hole if you want.