Liberty comes from the Latin word libertas, which means “unbounded, unrestricted or released from constraint.” Libertas even contains the idea of being separate and independent.
The English word Freedom can trace its roots to the Germanic or Norse word Frei, describing someone who belongs to a tribe and has the rights and protections that go with belonging. Besides freedom the root frei becomes the English word friend.
To have liberty is to be unencumbered.
To have freedom is to have the aggregate benefits and protections provided by society.
As citizens we give up some of our liberty in exchange for freedom. This is the social contract. It allows us to enjoy our liberty far more than we otherwise could. (Being unencumbered isn’t much fun in a lawless place like Sudan)
Freedom is given by society to its constituents. For example, our society provides medicine, education and rule of law (among many other things). Any one of these would be far less valuable without any other. Therefore the aggregate is more than the sum of its part, so the word “freedom” has its own unique meaning.
There is no other word for this concept, and by forgetting the meaning of “freedom” we have lost some of our appreciation that which unites us.