If you understand the terms:
then you have, possibly, the ability to understand the term "chef", the French spelling of the English term of "chief".
Otherwise, IMHO, your education is deficient, there is NO relationship between the term "chef" and "culinary ability". There IS a direct relationship between running a successful culinary enterprise and the term CHEF, it is identically equivalent to C.E.O., nothing more, nothing less.
Now, if you desire, a case might be made for a "culinary skill" designation along the lines of:
- Apprentice Kitchen helper
- Apprentice Prep Cook
- Prep Cook
- Line Cook, or possibly, journeyman cook
- Station Cook, often termed "Chef de Partie" (though we are now entering the realm of MANAGEMENT!)
IMHO, there is absolutely NO relationship between "culinary skills" and "management abilities". They are two separate and distinct skill sets and occupational endeavors.
The finest and most creative culinary cooks may NOT be able to manage a business.
The finest and most creative business managers may NOT be able to produce the most creative and enjoyable culinary creations.
Remember, a Michelin "Star" is not earned by any one skill, it is a combination of factors.
Anyone who believes that the term "chef" means anything other than "boss of the kitchen" is sadly mistaken and doomed to failure!