Cosmetology is about all aspects of beauty, including haircuts, manicures and pedicures, makeup, skin care products. They might use machines or other tools in their work.
That would be the name for hair, skin and nails. There are schools all around the country that have such programs. If you go to a beauty parlor to get your hair done that is done by a cosmetologist. They are also the people who do hair skin and nails in movies and tv shows.