If a person actually dyes their hair red,can you call them red heads? Or does that mean their Ginger?

This girl I know dyed her hair red,As I was describing to my friend,this gorgeous girl, I used the term red head ,since she has bright red as her chosen colour,My friend suddenly exclaimed that she was a ginger! I said no she�s a read head.He insisted that "Red Head" is a term used for gingers.I say its used for people that have just red hair :/