Rousseau variously invokes "natural freedom," "civil freedom," and "moral freedom." Burke invokes "irrational liberty," "regulated liberty," "constitutional liberty," and "civil liberty." I have two questions.
I can only give you a partial answer on rousseau's true freedom. I know that in his book Du Contrat Social, he explains how we go from our natural freedom to our civil freedom and that our natural freedom is the freedom of doing anything without the law. Which means the natural freedom is living a savage life. Therefore there is no evolution to ths human race. So a civil freedom is more important for Rousseau because it gives the people a way of living and being with the help of the law. He explains in details the concept of the law as scarier than anything for the citizens and explains why it gives us evolution in his book. Im sorry if i dont completely remember my readings but I loved the book and I recommend everyone to read it.
