But only if you limit your thoughts to the words “cosmic rays” and “gamma rays.”

You said:

“Cosmic rays are actual high-energy particles, mostly protons.”

That is true.

You said:

“They interact with matter in a much different way than gamma rays (high energy electromagnetic radiation) do.”

That is true:

You said:

“The two are apples and oranges.”

Apples and oranges grow in trees, both types of “rays” originate in atoms.

You said:

“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.”

That is true.

You said:

“They have nothing to do with radioactive materials.”

Here I disagree with you on the word “nothing.”

I Googled Gamma rays and found this site: http://www.answers.com/topic/gamma-ray

It says about the gamma ray:

“Penetrating very short-wavelength electromagnetic radiation, similar to an X-ray but of higher energy, that is emitted spontaneously by some radioactive substances (see gamma decay; radioactivity). Gamma radiation also originates in the decay of certain subatomic particles and in particle-antiparticle annihilation (see also antimatter). Gamma rays can initiate nuclear fission, can be absorbed by ejection of an electron (see photoelectric effect), and can be scattered by free electrons (see Compton effect).”

I emphasised the part that seemed important.

Google turned up this site on radioactivity: http://www.answers.com/topic/radioactivity

The radioactive series decay seemed also very interesting.

“In a number of cases a radioactive nuclide A decays into a nuclide B which is also radioactive; the nuclide B decays into C which is also radioactive, and so on. For example, 23290Th decays into a series of 10 successive radioactive nuclides. Substantially all the primary products of nuclear fission are negatron beta-particle emitters which decay through a chain or series of two to six successive beta-particle emitters before a stable nuclide is reached as an end product.”

As I understand it, in each successive decay of a radioactive nucleus there is “gamma radiation” associated with it, and also “particles” such as those associated with cosmic rays.