To understand what is happening inside the nucleus, we need to understand more about the quarks that make up the protons and neutrons in the nucleus. Quarks have electromagnetic charge, and they also have an altogether different kind of charge called color charge. The force between color-charged particles is very strong, so this force is "creatively" called

The strong force holds quarks together to form hadrons, so its carrier particles are whimsically called gluons because they so tightly "glue" quarks together. (Other name candidates included the "hold-on," the "duct-tape-it-on," and the "tie-it-on!")

Color charge behaves differently than electromagnetic charge. Gluons, themselves, have color charge, which is weird and not at all like photons which do not have electromagnetic charge. And while quarks have color charge, composite particles made out of quarks have no net color charge (they are color neutral). For this reason, the strong force only takes place on the really small level of quark interactions, which is why you are not aware of the strong force in your everyday life.