free·dom
ˈfrēdəm/
independence,
self-government,
self-determination,
self-rule,
home rule,
sovereignty, nonalignment,
autonomy;
democracy
"revolution was the only path to freedom"
antonyms:
dependence
- the state of not being imprisoned or enslaved.
The definition for freedom is correct, but your definition of liberty is false.
Liberty refers to what you are permitted to do by the government. When you are at liberty, you are not party to a contextual restriction by the government. There is evidence in how the word has historically been used.