Why is milk called
dairy milk on this milk carton?
I suppose the basic reason is because it comes from a dairy.
Anyway, the usage of the word milk is a larger issue, as there are other products such as almond milk or soy milk that don't come from cows.
Some "dairy" milk concerns say these products shouldn't be able to use the word milk to describe them. Supposedly the "dairy" milk companies don't want to lose market share to the similarly named products, so labeling becomes important.
By definition you can find both cases. See milk.