Eating "clean" for me constitutes a diet that does not contain a huge proportion of processed crap.
I say "huge proportion" since I do, on occasion, eat such things as Mike-n-Ikes, red vines; you know, candy. Also I drink beer. But I don't drink sodas, bottled fruit juices or eat pre-packaged foods.
So, 95% of my diet is pure, unadulterated food. Vegetables, red meat, poultry and a mix of low/high GI carb stuff (fruit, oatmeal, potatoes, whole grains, etc.).
With plenty of water thrown in.
So, I guess you could say "well" and "clean" are somewhat similar in meaning. However "well" and "clean" in diet may vary according to the individual.