I’m sure some physics guru will give you a more technical answer but here’s a mechanical engineers understanding.
Is light a wave or a particle (photon)?
Answer: It depends on how you look at it.
Seriously, that’s what causes this paradox. If you observe light as a wave with experiments that observe the behavior of waves like diffraction then light is a wave. Its wave length can be shifted, like in the doper effect, and it can be separated with a prism (diffraction). Now if you look at light as a particle (photon) it will behave as such. A single photon can be detected and counted.
So, if that’s not confusing I don’t know what is.
The simple truth of the matter is we do not know exactly what physical stuff light is made up of. We can measure many of its properties and describe it physically but we cannot get away from the particle-wave duality.
I realize your question focused on what is a wave. A wave in the ocean is easy to see and understand. Now an energy wave traveling through time space - well that is much more of a stretch.
***Once again, the wave properties of light are analogies and relationships that describe the observable behavior of the light.****
It does not and will never tell us what stuff it is made of or even how it does it.
It is very difficult to accept something so intangible. I think if you just accept a light wave is an analogy to its behavior under one type of observation and that analogy doesn’t work under a different type of observation then it may be easier to accept how little we know about what it is.