In fission a heavy nucleus such as uranium-235 absorbs a slow neutron and splits into two medium nuclei, releasing two or three neutrons and about 200 MeV. These neutrons can cause more fissions, which is a chain reaction. A reactor keeps it steady with a moderator, control rods and a coolant.
In fusion light nuclei join to form a heavier one. It needs a very high temperature so that the nuclei can get close despite their electric repulsion. Both processes release energy because mass is lost.
Radiation ionises matter. This is how detectors work and why radiation harms living cells. Absorbed dose is the energy absorbed per kilogram; the equivalent dose also allows for the type of radiation.