They are generally synonymous in common usage, but more precisely freedom is the lack of requirement to do something, while liberty is the ability to do something.
So for example you might have the freedom to cross state borders without being searched, and you might have the liberty to speak your mind about the government.
The word freedom stems from the Germanic language family whereas the word liberty is from the Latin / Romance / French language. They mean the same thing and are synonyms. I guess liberty is used in more formal situations. A lot of the technical / formal terms used in the English language are derived from Latin and Greek.
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