Liberty or Freedom?

Both words mean the same; and one can used in place of the other. What it make different?
For example, if have a pet you can named Freedom or Liberty?
Talking about of the: Statue of the Liberty or Statue of the Freedom?

The two words are certainly close enough in meaning that you could call your pet either Freedom or Liberty. But, it’s the Statue of Liberty, not the Statue of Freedom. Although it could have been called the Statue of Freedom, once it had a name, then it is referred to by that name. Just as your pet wouldn’t come to Freedom if you started out calling it Liberty.