I wave my particle

The word "quanta" in this context means discrete units of energy. It is a general term; in the case of electromagnetic energy a quantum is a photon.

Mindbogglingly, light behaves as both particles and waves, not neither. The best explanation I've seen for this so far is this video about quantum fields.

A photon is a quanta of light. Our picture of light, to this point, has been that of a wave. Wave-like characteristics are responsible for diffraction and refraction. However, light is absorbed and emitted one photon at a time.

I knew some new study would betrayal me, well I still wave my particle.....

Or both

Quanta is just a word (related to quantity) as in: "smallest divisible quantity of"

So in the case of light we would be talking about photons, which are a quanta of light (e.g. discrete "packets" of light).

Light behaves as a wave, e.g. we can talk about the frequency of light. But it's also pretty different from macroscopic waves e.g. it's not accurate to think of them as what your see on a typical sinusoid graph, as at that level things don't really have a fixed shape or position, we're talking more about areas where they "probably" are (see: superposition, HUP etc)

It's useful to think of light in terms of discrete photons for a number of reasons, e.g. in pair production, 1 gamma photon would be sufficient to create 1 electron/positron pair.

Photons also exhibit other particle-like behaviour despite having no rest mass. But the idea of rest mass becomes less significant at that level anyway as the line between energy and mass (e=mc²) gets blurred. And any sufficiently high energy object will likely exhibit some massive properties (hence why we tend to use MeV - a measure of energy - instead of a measure of mass, even when performing calculations with massive particles such as electrons.