Cosmic rays
Cosmic rays are actual high-energy particles, mostly protons. They interact with matter in a much different way than gamma rays (high energy electromagnetic radiation) do.
The two are apples and oranges.
The gamma rays originating in thunderstorms seem to be a function of high-powered electrical discharges, producing a similar phenomenon to the generation of X-rays by bombarding a target with electrons.
They have nothing to do with radioactive materials.