Question

Chef and cook positive or negative connotation

Answer 1

Chef is positive notation and cook is negative notation

Answer 2

Chef has a positive connotation because the term "Chef" is usually used to describe a person who has undergone culinary school and works in an upscale restaurant or as a private chef. A cook is typically seen as a lower skilled chef and therefore has a negative connotation.
This is a good reference:
https://www.reluctantgourmet.com/difference-cook-chef/