A hairstyle is just one part of a woman's hairdo. A woman might have a hairstyle that is traditional, modern, or somewhere in between.
She has a very traditional hairstyle, with her hair pulled back into a bun.
She has a modern hairstyle, which is a little more loose.
She has a hairstyle that is somewhere in between, with her hair pulled back into a bun and some of it left down.