"Waves" is generally, are oscillations which occur in a medium.
A photon is a particle. E&M Radiation can be described as particles (photons) or as waves which are oscillations in the electric and magnetic fields in whatever region you are considering. Light waves are most certainly an actual thing, that exists in space, and can be measured etc. "Physical" is a tough word to use, i'm going to avoid it.
What you're referring to is a wave function to describe particles (especially electrons, but it does apply to photons for instance, as-well).
What a wave-function really is, is up to debate/interpretation. A Wave function is definitely tied to the probability of finding a particle at a particular place, with a particular energy, momentum, etc.
Whether the wave-function is purely a mathematical construct, and merely a way of THINKING about actual things... is a hard question to answer.
I would say, that wave functions are actual things: oscillations and locations of probability. But you definitely can't measure/touch/interact with the wave-function in-and-of itself.
Start from what is observed: Poisson's spot (Arago spot), interference, etc. From this, a mathematical construct which accurately describes the phenomena can be created.
Applying the construct to new phenomena (frustrated total internal reflection) may or may not be strightforward, but that is a statement regarding the (artifical) construct, not on the underlying phenomenon.