Why in korean head/hair are the same?

I have a doubt with this word '머리', would it be any different if i want to say "she cut my head" and "she cut my hair"? Would those sentences be the same in korean?

Im on mobile so i cant write long but i have a few tips for you. "hair" is 머리,머리카락,두발 etc. but when you talk about a hair cut, you can say 머리자르다, 머리하다,미용실가다,커트하다. 

Women often cut only their front part of hair. In this case u can say 앞머리만 잘라주세요.

머리카락 usually means one hair/a few hairs.

As a child, I wondered about this too.:)