Liberty
Liberty is the condition of being free from any form of arbitrary control. The term is closely related to Freedom and is sometimes used synonymously with that term, however, freedom usually also refers to having the ability or means to express liberty to a desired or specified extent. The word may also refer to a specific granted freedom, e.g., liberty granted to sailors while at port.
Hypothetical example
To differentiate the the two terms, freedom and liberty, take a hypothetical example of a society in which all real property and all roadways are privately owned, and all owners have unimpeded leaway to control the use and access on their property. Now imagine that Bob owned a house in a housing tract along a road owned by Alice. For years, Alice has allowed all home owners to use the road for access to their property, but one day, while Bob was sleeping, she closed off access to Bob and anyone coming or going to his house. And the property-owners surrounding Bob's property also excluded Bob from using their property. Bob would be stuck on his own property and would not be able to leave, have visitors, or even get provisions to survive. Since Bob was not being physically or legally restrained he would have liberty, but because he could not exercise his liberty he would not have freedom.
Etymology
The word liberty comes from the old latin word liber, which later became libertas. This bacame the Old French word liberte which was introduced into Middle English during the Normanization of the language in the 11th century, eventually becoming the current form libery.
The use of the the word liberty instead of freedom in much of the writings of the founding fathers and in our founding documents may have been an homage to the French, as they were instrumental in the success of the American Revolution. This differentiation is also why we have a Statue of Liberty in New York Harbor instead of a Statue of Freedom, the statue being a gift from France in the 1870's.