What it is
Real cheese melted down and rebuilt with emulsifying salts into something uniform and meltable — and the name tells on the dilution: "cheese," then "cheese food," then "cheese product," each step further from the original.
Why your biology objects
Emulsifying salts (sodium phosphate and citrate) pull the calcium out of the casein so fat and water stay blended and it melts without breaking. The legal naming ladder is the receipt: "product" doesn't even meet the standard of identity for cheese. A re-engineered food, not an aged one.