I'm not sure that anyone really wants to know after reading this thread, but I'll give some possibilities anyway:
1). no scientist REALLY knows the answers to things like this as the actions are taking place at far too microscopic a scale to be directly observed. Science also tends to be very accurate at measuring HOW something goes [i.e. these elements in these conditions can produce X amount of measurable energy] but not so good at WHY something happens [i.e. where does that energy come from?]. We make theoretical models and hope.
2). The old way of looking at Fission was that all elements were composed, yes, of protons, neutrons, and electrons, but that wasn't the whole story. Because protons all have positive charges, it was always a conundrum as to how those repulsive "like" charges could remain packed tightly into the nucleus without flying apart. So, the theoretical model of a form of nuclear binding force [later called the "Strong Nuclear Force"] came into being. Calculations with the model suggested that every nucleus had its own "amount" of strong nuclear force [carried by a different class/conception of particles called "force-carrying particles"].
The nucleus of a Uranium-235 atom or a Plutonium-239 atom will, in this model, contain a certain amount of this force. When these nuclei FISS, they form two or more [usually two big pieces and two free-flying neutrons]. These smaller nuclei don't need as much of the binding force as did the big one. The force must go somewhere. It is essentially released as "LIGHT" in all its electromagnetic spectrum forms.
3). Fusion is different. The old model for this was that Hydrogen atoms, and specifically the Hydrogen nucleus [a single proton] could be crushed together only so far with another proton until it had to "give". The way it "gave" under the tremendous heat was that one of the two protons would be changed into a neutron. Neutrons and protons weigh nearly the same, but in the neutron the positive charge is gone. What happened to it? The model says it "escaped" as a very light positively-charged particle. A very light positively charged particle is a "positron", or more germanely, an antimatter electron. Antimatter won't last long in our matter universe, so it rapidly merges with a matter electron, and the two mutually dematerialize into pure energy, as to Einstein's equation. This energy is radiated away as the full spectrum of "LIGHT". including Gamma and X-rays.
As I say, this might well have been just a joke and nobody is really interested, but I'm an old teacher and Hope never dies.