electricity - What’s the relationship between thermal radiation and Johnson thermal noise?

All objects above absolute zero emit radiation due to random collisions between the atoms they are made of. The spectrum of radiation emitted varies according to the temperature of the object, I believe because of the random speeds at which atoms hit each other, producing photons of random energies/wavelengths that follow a probability distribution. The energy and frequencies increase as the temperature increases. This is called thermal radiation, related to black-body radiation.

All electrical components create small noise currents due to the random thermal motion of electrons they are made of. The current/voltage level increases as the temperature increases, with a constant white spectrum. This is called thermal noise or Johnson noise.

What's the relationship between these? Are they created by the same process? Why are their spectra different?