Casein is the main protein in milk (there are other proteins
in milk and these occur in smaller quantities).  People
can have many different types of reactions to casein or the
other milk proteins (anaphylaxis, headaches, arthritis,
kidney pains, fuzzy thinking, etc., etc.)

Lactose is the sugar in milk and people without the enzyme
lactase in their gut have difficulty digesting lactose.
They are said to be lactose intolerant.  They will get gas,
stomach pains, diarrhea, etc.

There are other possible sensitivities and allergies but I
hope I have answered your main question.  Welcome to the
list.