This is a great video. Basically the three major elements for coral growth as well as the health of every living things in the tank is Carbon, Nitrogen and Phosphorus.
The major inputs of these elements for coral are as following:
Carbon source: food, alkalinity, dissolved organic compounds. Food accounted for majority of the carbon input, including the nutrients produced by symbiotic algae, food particles captured by coral. Alkalinity is also provided a large portion of carbon needs.
Nitrogen and Phosphorus sources are from food (again), dissolved organic compounds, and lastly but not significantly from actual nitrate and phosphate in the water.
So, Nitrate and phosphate only accounted for small portions of total N and P intakes.
Since we can’t accurately test how much dissolved organic compounds in the water at a hobby level, which play far more important roles than Nitrate and Phosphate, that leads to all the different observations from different tanks.
These days, I will look at Nitrate and Phosphate testings as a small grain of salt, just make sure they are not too high.