From what I've picked up separate waves describe what is happening in typical Covid-19 patients: immune reactions that are good enough against the virus in the throat are insufficient to defeat it elsewhere so you get a first wave in the throat and if the virus spread into the lungs before that wave is over there's a second wave in the lungs. That wave then requires a different or stronger immune reaction.

For the flu, absolutely. It mutates rapidly and one can get the virus, mount an effective defense, and then the virus mutates and escapes the immune defense. This happens. It is known that coronaviruses mutate much more slowly than influenza for fundamental reasons. It is highly probably but not proven that this much slower rate is sufficient to preclude the "waves" you refer to.

It is a totally unrelated virus, but if you get chickenpox you may get many years later shingles, the virus may remain inactive in nerve cells fo a long time. https://en.wikipedia.org/wiki/Shingles

What a strange game of life