My Grandfather/Father called me his granddaughter and it hurts.?

I understand why you're hurt, but it's not his intention at all, and it's not a denial of the very wonderful and special relationship between the two of you -- you referring to him as Daddy is actually a very sweet and personal thing, when he talks to other people and says he's your grandfather, he's just stating a fact, it's not any reflection on your relationship with him. You know, a wife could call her husband Bo Bo Bear when they are alone as an expression of love and affection, a special, private name, but when they go out, she had better not say, and I'd like you to meet my Bo Bo Bear Steve!! You sound like a very intelligent and sensitive young woman, and you're going to be vulnerable to a lot of things when you are that way, but you're also going to understand, appreciate and enjoy a lot of things that fly right over other people's heads, so start considering things from that point of view, and work on gaining perspective in such situations so that you don't end up hurt when you don't have to -- good luck! (and you and your parents are blessed!)