It works like this:
Nuclear reactions produce radiation. The reactors are built to sheild that radiation. Run properly, no radiation excapes into the area surrounding the reactor.
Coal combustion, (along with many other reactions) does produce a small amount of radiation. It is much smaller than the radiation released by nuclear fission, but there is some radiation. The high volume of coal burned in a coal power plant, combined with no attempts at sheilding radiation, results in a release of some radiation to the environment.
It’s not that coal releases a significant amount of radiation, it’s the fact that nuclear reactors are heavily sheilded, while coal plants aren’t.