this is the best definition and description I can come up with:
A cook is judged by what they put on a plate.
Period, end of discussion.
A Chef is judged by how well they manage the resources of the kitchen.
Look this discussion does not take place in continental Europe, no cook calls himself a Chef. I did a cook's apprenticeship in Switzerland. 3 years of split shifts. At the end of that time there was 2 days worth of written exams, then the final practical, cooking a 6 course meal for 10 people in under 4 hours followed by another two hours of practical "show me how's". After a month of nervous waiting, I get my papers in the mail. They state "Cook" in all 4 official languages of Switzerland. No mistake about what to call myself.