In the mini series "Chernobyl" first responders who were exposed to radiation at the scene had to be quarantined. Why? My understanding is that when Uranium 235 fissions it releases nuetrons and gamma energy. The gamma enery can penetrate the skin and 'ionize' compounds in our bodies (bad) as well as break checmical bonds in our dna (also, bad and maybe not a different thing). So that explains why direct exposure is bad, but what is the mechanism for them continuing to be dangerous to others around them? Is fissioning Uranium somehow in their body?
Used nuclear fuel contains fission products like cesium-137 and iodine-131. When that escapes from the core of the reactor surfaces, clothes, food, dust etc will get "contaminated" with radioactive isotopes. People will ingest and inhale these. Unhealthy.
But there is no infection. After a shower and clean clothes, such people are not a danger to others. However, it seems that people from Hiroshima and Fukushima were shunned like bearers of contagious diseases. Very strange, but possibly due to unfortunate jargon like "contamination".