First of all, no they are not the same thing close but not interchangeable. Food cost percentage is the amount of money you spent on food to make the dish you sell. Period. End of story.
Cost of Goods Sold- refers to all expenses incurred in selling a product. Cost of goods sold can include paper napkins, to-go containers, a percentage of rent or administrative fees and sometimes labor.
Food cost percentage is more of an operations management issue while COGS is a macro business issue. You may be the one managing both of these but separating them out in this way helps to master the concept more.
The formula for a food cost percentage is: Sales price/cost of food= food cost percentage