The critical role of proper nutrition with intense exercise use regimens cannot be overstated. The fitness industry is rife with myths, misinformation, faith based beliefs, inconclusive studies, and real hard science.
The role of protein supplements for strength and muscle building adherents is very well researched, and the abstract linked below published in the Journal of Strength and Conditioning is further evidence that if your exercise routine places you in the above categories, you should supplement.
The human body is a giant chemical factory. Whatever you consume is broken down into its simplest chemical components before it can be absorbed and used by the body. All carbs are turned into simple glucose before they can be used. Pasta, bread, rice, apples, and broccoli, are all turned into glucose, and whatever micronutrients they contain (vitamins and minerals) before they are usable by our bodies.
Likewise, proteins are broken down, but instead of glucose, proteins are turned into amino acids (plus whatever micronutrients are present) before they can be absorbed. Some proteins can be broken down more quickly than others, just like some carbs can be broken down faster than others. Sugar is so close to glucose its almost instantly absorbed. Whey is so close to digestible form it to is rapidly broken down into amino acids and absorbed. Taking amino acids directly that the absorption, like sugar, is almost instant, allowing for precise timing for maximum benefit. With this introduction by me, read the science:
Fitnessgroan's Blog 
Are there any general set of conditions between someone who needs to supplement and one who does not? When I get back from exercise I drink a big glass of milk. Would that be considered a supplement or do I still need to add whey?
T
It really depends on your goal, and whether or not you find yourself getting frequent colds; often around hard training days. Milk possesses a high percentage of whey (about 30% of milk protein) song or you it’s probably enough assuming an otherwise healthy diet with sufficient protein intake:
Approx 1gm protein/kilogram of body weight.