No, the confusion does not come from confusing these words. They are synonyms for the same concept.
freedom: the power or right to act, speak, or think as one wants without hindrance or restraint.
liberty: the power or scope to act as one pleases.
Liberty certainly doesn't deal with "justice". Justice is its own concept.
Generally, people who talk about liberty and freedom being different things are trying to undermine the concept of liberty because they don't really want people to be free. They want people to behave as they would wish them to behave. So they try to say "freedom" really means doing what I want you to do.
These words were not synonyms to the founding Fathers. No one said, “Give me Freedom or give me death!” They were fighting for God-given rights. After the Civil War the term was changed from liberty to freedom - and that is the word we use today. But they are not interchangeable in their historic context.