Does the nuclear reactions in an element like Uranium produce a different amount of energy than the nuclear reactions in Plutonium? I am not concerned with those elements in particular, they just seem to be the most common. And, if they do produce different amounts of energy, why and how? Thank you much.
The energy produced in a nuclear reaction is proportional to the difference in rest masses between daughter nuclei (final products) and the initial nuclei (in your example one nucleus and a neutron). Because different nuclei decay into different nuclei, and because the binding energies that determine the rest masses of nuclei are of complicated nature, it would rather be surprising if two different reactions released the same energy. So in short there is no reason for the energy to be the same for different elements.
As an analogy consider an atom. Atoms are objects made up of particles (electrons and nuclei) and they have a variety of excited states, which we can with some effort calculate using quantum mechanics. Transitions between these excited states release energy (as light). The excited states of a hydrogen atom are not the same as the excited states of a helium atom because, well, the atoms are different. Hydrogen has one electron while helium has two. And because their excited states are different the energy emitted, i.e. the spectra, of hydrogen and helium are different.
This argument carres over to nuclei as well. Nuclei are also made up of particles (protons and neutrons) and they also have excited states, though actually calculating these excited states is currently too difficult to do except in an approximate way. Transitions between excited states of nuclei also release energy and again it's as light (gamma rays).
Nuclei manage a trick that atoms don't usually do, which is that they can break up to release electrons and/or alpha particles, or indeed they can fission into two. Just as with gamma ray emission the exact way the nuclei fragment, and the energy released, depends on the quantum states of the nuclei and they decay products.
And just like atoms, different nuclei have different states because they contain different numbers of particles. So the energy they release is also different. For example a uranium nucleus undergoing alpha decay will release a different amount of energy to a plutonium nucleus undergoing alpha decay because, well, they're different.