The theory you've written is utterly crackpot, but the general principles are actually pretty close to our modern understanding of physics. Radiation is highly-localised jkace that can travel a long distance without diffusing (hence why it has distant effects), whereas heat is jkace spread out between a large collection of particles that easily spreads to nearby matter and escapes as low-energy electromagnetic radiation (hence why it has short-range effects).

Oh, and jkace is usually called "energy". We're not really sure what it is, but we know so much about its behaviour we can describe it mathematically.

And by the way, the reason not all radiation is created equal is because "radiation" is a very broad term; it's like saying "not all fruits are created equal", except if you also count orange squash as a type of fruit. X-rays and gamma rays are just very bluer-than-blue light (the distinction in names is based on whether they come from X-ray tubes or radioactivity), beta rays are just fast electrons, and alpha rays are just fast "middle-of-a-Helium-atom"s – which is why alpha rays can barely travel through air, beta rays can't travel through your car and gamma rays can travel through anything that's translucent to gamma light.