It's basic biology, same as plants in theory, but potentially different in exact action. The coral is producing food for itself to help growth. Now, if it's creating carbohydrates as a coral as it would if it were a plant, i'm not sure there -- But it's creating energy regardless.
In the wild, corals have a lot of food in the water column, and in Biggles videos you can see HD closeups of polyps actively ingesting food flowing through the water. This is why in some countries (EU, notably Italy) that Phytoplankton systems are a HUGE market -- In Italy it's nearly considered essential if you're trying to maximize growth, as it gives the coral what simple photosynthesis cannot.
As for photosynthesis itself, it's a living animal, so it's making what it can to survive. This allows it to more readily take up calcium, alkalinity and Magnesium to create a coral skeleton and accelerate growth.
As for par, corals in the wild develop zooxanthellae to basically give themselves shade from the unrelenting sun. This is why so many wild colonies are darker colors, and colorful corals are more rare -- More colorful corals fail the survival of the fittest test. When the water gets hot during summer, and the sun is beating down on them, the lighter colored corals are less likely to survive than the "green dogs" -- This is because the darker corals with more zooxanthellae are better protected from the sun. This is doubly useful, as it also increases their rate of photosynthesis due to the increased number of zoox (more engines churning out energy).
This means higher par is more likely to cause your corals to darken up. This is also exacerbated by nutrient levels, so it's harder to find the intersection of where Par & Nutrients collide to give = Color.
Color. If lighting is too intense too fast, coral start losing tissue. Although if one were to gradually raise lighting intensity you'll see corals begin to darken before they die, or at least attempt to darken. In a tank, this is much harder than in nature, as in nature they have significantly more energy at their disposal than we give them not only from the suns spectrum, but because the suns intensity, and the fact that most of the extremely hardy corals are what we don't collect -- because of their seeming lack of color. The phytoplankton is also a factor, we force them to only rely on photosynthesis, which hampers their potential as well as survival in times of duress.
