But “phase” is a comparison of two waves, their frequency can be the same but their undulating time period is shifted from each other.
In a color TV transmission the color information is inserted as a phase shift of a sub carrier.
In the receiver you have a synchronized reference oscillator that allows you to decode the phase shift and translate it back into color information.

When you mention waves, all types of words come to mind that have some reference to wave action.
Wave forms or shapes such as, sine, square, triangle, saw tooth are important in electronics.
Saw tooth waveforms have been used in TV sets for creating the raster and the high voltage for the CRT.

Undulations,
And alternating change in environment, such as a heat waves come to mind.

Longitudinal and transverse waves. are interesting.

Doppler effect and sonic boom is another interesting subject.

There is also speculation that the Rayleigh surface waves were used by the Egyptians to move the building blocks for the pyramids.

I suspect that the wave motion of electrons and protons create the charges within atoms.

No matter what type of a wave one studies, it becomes clear that motion or activity of some type or another is involved.
Energy is another word that refers to some type of a motion, without motion there would be no energy.
Energy = (potential / kinetic) * constant.

At what point did you say MEGO ? :-}