What is the difference between being charming and flirty?

Charming is knowing how to flatter and ingratiate yourself without having to throw yourself at someone (flirting)

When someone is charming they have admirers for their charm and personality.

When someone is a flirt, they have admirers who look at them more for physical reasons.

Charming would be a comment such as, Wow, you look great in that shirt, the colour really brings out your eyes

Flirty is more along the lines of, Wow, you look great in that shirt, bet you would look better with it off though, wink wink!