The following definitions were taken from Merriam Webster Dictionary via Merriam-Webster.com.
liberty
lib·er·ty | \ ˈli-bər-tē \
plural liberties
Definition of 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 (see DESPOT sense 1) control
d: the positive enjoyment of various social, political, or economic rights and privileges
e: the power of choice
2a: a right or immunity enjoyed by prescription or by grant : PRIVILEGE
b: permission especially to go freely within specified limits was given the liberty of the house
3: an action going beyond normal limits: such as
a: a breach of etiquette or propriety : FAMILIARITYtook undue liberties with a stranger
b: RISK, CHANCE took foolish liberties with his health
c: a violation of rules or a deviation from standard practice took liberties in the way he played the game
d: a distortion of fact The movie takes many liberties with the actual events.
4: a short authorized absence from naval duty usually for less than 48 hours
freedom
free·dom | \ ˈfrē-dəm \
Definition of freedom
1: the quality or state of being free: such 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: unrestricted use gave him the freedom of their home
e: EASE, FACILITY spoke the language with freedom
f: the quality of being frank, open, or outspoken answered with freedom
g: improper familiarity
h: boldness of conception or execution
2a: a political right