Just a hunch, but a make up diploma is a fancy piece of paper. Which is not a license, nor would it license you to work in a salon/spa or as a freelance make up artist in a state that happens to require a license to charge for make up services (all states are different).
Esthetician deals with just the face/skin, cosmetology is hair (along with skin, I believe, don't quote me).
No clue about this school, but maybe see if you can find an established MUA (whether you want to do print work, bridal, movies, etc) in your area you can intern with. You'll gain experience and make connections as you go.