When people say that a photon is a quantum of light, are they talking about 2 different types of quantizations in one phrase? To quantize something, you take something continuous and make it discrete (more or less). Energy in a light wave of frequency $f$ is continuous in (1) value and (2) location. The energy is distributed over space and if you fiddle with the amplitude knob, you can make its energy vary continuously to any value that you want. To say that its energy is quantized into steps of $hf$ means that the energy of the wave cannot vary continuously as you fiddle with the amplitude knob. The energy can only bounce between different $nhf$ levels. However, this doesn't mean that the energy has to come in packets? I can imagine a wave with quantized energy $nhf$ distributed continuously over space (therefore, its energy is quantized but the energy is not spatially quantized into packets. Physically, from a classical perspective, quantizing energy doesn't make sense. However mathematically/logically, quantizing the energy of the wave but not quantizing the location of the energy is completely fine. See signal processing: discrete amplitude signal + continuous time domain, or discrete domain + continuous range, or both discrete amplitude and discrete domain in which case you have a completely digital signal). On the other hand, to say that energy hits you in packets (instead of hitting you continuously as in classical physics) doesn't imply that the energy of those packets has to be quantized.
So a photon is light energy quantized in value and energy quantized spatially?
I ask because I think the terminology gets confusing across different sources and people. From what I gather, when people say a wave is quantized (or something along those lines), they already have wave-particle duality in mind. So in the back of their mind, they already quantized the spatial location of the energy (into particles). Therefore when they say 'quantize the wave' with the previous sentence already in mind, they specifically mean the value of the energy.