As names go The President's Daughter is definitely one of those that I will never respect, because it's named directly after only one version of itself, when the actual definition is cosmetically broader.
IMHO a Holy Child is much more of a "thing" than The President's Daughter. TPD isn't desirable for who they are, but instead used to manipulate the ones responsible over them. HC can go either way — they might actually have powers or value beyond their connections.
I can see a difference between one being important for what they are and possibly what powers they have, and the other for what connections they have. I don't think the descriptions support that, though.