I believe there is a fundamental difference, not in the linguistic history of the said terms (of course there is one), but in the modern American literal meaning(s).
Liberty-basically the ability to be able to do the right thing, as one perceives the right thing/action to pursue/perform.
Freedom-well, a lot here really. I think in general, it'd be the absence of barriers when planning and performing whatever it is one wishes to do.
Officially: liberty-1: the quality or state of being free: a: the power to do as one pleases b: freedom from physical restraint c: freedom from arbitrary or despotic control d: the positive enjoyment of various social, political, or economic rights and privileges e: the power of choice
freedom-1: the quality or state of being free: as a: the absence of necessity, coercion, or constraint in choice or action b: liberation from slavery or restraint or from the power of another : independence c: the quality or state of being exempt or released usually from something onerous <freedom from care> d: ease, facility <spoke the language with freedom> e: the quality of being frank, open, or outspoken <answered with freedom> f: improper familiarity g: boldness of conception or execution h: unrestricted use <gave him the freedom of their home>
Me and the MW dictionary