Food Allergies Treatment

Both can be devastating.
First, both are different. Milk allergy is caused by proteins in milk while lactose intolerance is inability of your body to digest lactose causing bacterial fermentation in your intestine and causes symptoms such as bloating, diarrhea, weight loss, and malnutrition. As I said both can be devastating.
From allergy, the worst you can get is anaphylactic shock while lactose intolerance might cause you severe malnutrition (i.e. marasmus and/or kwashiorkor).

they’re the same it’s just easier for a lactose intolerant person to say alergic to milk because all diary product is a form of milk.