In both cases the atomic nucleus breaks apart and gives off energy, the only difference that I can think of is the quantity of energy released per unit of time, the chain reaction also radiates very actively.
Why would you need three different words to describe the same basic function of decrease in the size of the nuclei and the subsequent high velocity emission of nuclear parts and gamma rays?
I agree with you on the point of combustion; you write:

“The energy from combustion comes from the rearranging of the electrons in the carbon and oxygen atoms before and after the combustion.”

But I think that you should define the nuclear reaction a little better; you write:

“The energy in the uranium comes from the rearrangement of protons and neutrons in the uranium nuclei.”

I also agree that the rearrangement of protons and neutrons in the uranium nuclei occurs, but there is much more going on than that.

Because the protons and neutrons fly off from the nucleus at very high speeds, they also penetrate into the adjoining atoms that are not breaking apart naturally, but once the neutrons or protons are captured by the atomic nuclei those atoms will also start to break apart, in other words, the non radioactive material adjoining the fission material also becomes radioactive.

If non radioactive material is made radioactive, then that newly radioactive material contains more energy than it did before being radioactive. Since heat is tied to the motion of molecules and molecules are made of atoms, if those atoms start to break up, then obviously the molecules will be subjected to more energy and therefore they will move/vibrate faster making them hotter.
Depending on the type of material that has become newly (more) radioactive, this extra energy from it can be very high or not so high per unit of time.
This EXTRA energy that has been ignited in non radioactive elements has been distributed into the biosphere during the nuclear age, and it has not been accounted for anywhere that I can observe on the internet.

Now imagine that we build a coal or oil furnace that contains 4,109.05 Terawatt hours of energy and we burn it at that energy level for more than fifty years, how hot would the surrounding of that furnace become and what would happen to the heat energy during that time period?

Hmm... you wanted the explanation to be simple, how about the following explanation.

During the nuclear age we have converted mass into energy and distributed the energy into the environment. Since energy can not be destroyed I would like to have confirmed evidence as to what has happened to the energy.