Yes, Skim milk does have casein protein in it.
The mix is roughly 80 / 20 where Casein makes up 80 percent of the liquid and Whey protein the remaining 20 percent.
And whilst this may seem like a good compromise, and maybe a cheaper alternative to buying Casein protein, cheaper is not necessarily better.
Slow digesting Casein protein is a far better option than skim milk especially if you’re sensitive to lactose.
Moreover, most people have a mild sensitivity to lactose, which can cause gas and as such stress your body which could lead to storage of fat, which is definitely the last thing you want to do.
Given skim milk has Whey protein and depending on how many carbs you ingest with it at the same time, you could unknowingly spike your insulin levels to a point where your body stores your much needed protein as fat. Try Gold Standard 100 Casein here.