You can read the Phyto chrome article here on the BR.
It's the only article ever written by a hobbyist for planted tanks on the topic.
I'll be adding to this as I just went through two grad doctoral level core classes on Phytocrome and light photoreceptors. One of the researchers had some nice diagrams that will explain the concepts much better and I can use them to better explain how a plant precieves light and can actually tell the difference between a piece a wood shading it, and another plant just based on the light itself.

Light will upregulate genes in response to the environment in a nut shell. These genes are interelated to many functions and light types, situations etc.
This allows plants to grow, flower and live in many habitats.

Algae also have very similar photochromes and cryptochromes. Thus these are highly conserved genes evolutionarily. Must be of some use likely.

Color temps on the other hand, they are our preception of light, not photosynthesis. When we buy lighting, we buy it general based on the way it looks to our eyes, not on plant growth.
The vendors know this and sell that, because, well, that's marketing for ya


Regards,
Tom Barr