A "ray" in geometric optics is a locus of continuous propagation of light. Think of it as mapping where the energy is going in space. In principle there are an arbitrarily large number of them, but we draw a manageable number for visualization purposes.
The various [letter]-rays were so named when people didn't know what they were beyond being things that carried energy. X- and gamma-rays are high-frequency light. At those frequencies it is generally easier to use the photon picture to get a comprehensive understanding of how they work but they are still light. (Alpha-, beta- and delta-rays are sub-atomic particles, not light.)
You seem to be very hung up on getting some kind of concrete analogy for the nature of light. That's going to be a problem because light isn't like the things that you are used to at human scale. It acts like light.
Physicists use several different model to talk about light depending on the circumstance.
- Ray are used in geometric optics.
- Photons are used where quantum effects are important.
- Maxwell's equations and the resulting wave equation are used in lot of cases, and comes in several approximated forms (near fields, far fields, ...).
All of these tools capture some features of the behavior of light and are shaky on others. Each of them gives a partial understanding. By picking the right tool you can get "close enough" for a particular situation. Physic is all about "close enough".
Learning how to uses these models and how the correspond to one another is a big job and you aren't going to get it right unless you are able to look beyond analogies.