Neither chefs or cooks require "papers" to call themselves either. Anyone can call themeslves a cook or a chef.
Apart from that .........
IME, "chef" is an honour bestowed upon those that have excelled in a "respectable" kitchen. It is awarded by the primary chef, and celebrated.
FYI I know people who did whatever "cooking course" (and their grunt in the kitchen) and still 20 years later call themselves "cooks". I know them because their food is outstanding.
I love both "chefs" and "cooks".