'Liberty' is a more explicitly political concept to me, in keeping with Latin-derived words tending to have more specific connotations.
But in American political parlance, you hear "freedom" used as often as liberty, if not more.
Think of FDR's "Four Freedoms" or Dubya telling us that the terrorists "hate us for our freedoms" or Mike Huckabee's "Faith, Family, Freedom" slogan or the whole "muh freedoms" meme.
I think Madeleine was saying that liberty is more explicitly political, i.e. they both are used in politics, but freedom is also used in other contexts. For example, most people would say "I have the freedom to do what I want now that I'm not taking care of children" rather than "I have the liberty to do what I want now that I'm not taking care of children."
