@electricangel. In theory, no. In practice, yes.
«We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness»
This is written by the same men that had slaves and decided that only white men with a good economic position could voete. What’s the catch?
The catch is that the words didn’t mean the same as today. The American independence, like the French Revolution, were bourgeois revolutions, that is, revolts against the nobles (who ruled the Ancien Régime) by the bourgeois (the wealthy men), who wanted the country to be ruled by them instead of by the nobles.
«All men are created equal» meant that nobles are not created superior so bourgeois can rule (the fact the poor ones could have political power never entered their heads).
Liberty had a very narrow meaning. It meant «the burgeois are entitled to have political power without the restrictions of the Ancien Régime»
«The pursuit of happiness» is a tough one but contemporary authors that intervened in the drafting of the declaration declared that it meant «the pursuit of money», that is, that the bourgeois could trade freely without the economic restrictions of the Ancien Régime. But they wanted a pretty phrase.
Ok, what is the problem? The problem is that there was a lot of rhetoric in this document. Liberty sounds like freedom (that is, doing whatever I want). The pursuit of happiness is not understood so it does not sound like anything but it is pretty. «All men are created equal» sounds like the modern concept of equality. This was supposed to be a propaganda document to justify the independence from Britain and the fact that the new country was not going to be an aristocracy but ruled by bourgeois (something completely revolutionary at the time).
The second problem is that this ended up being a religious document of the new official religion of the new country (this religion could be called «liberalism» and has different sects: classical liberalism, socialism, socialdemocracy, political correctness, etc.). So liberty (which sounds like freedom) and «all men created equal» (which sounds like modern equality) ended up becoming religious dogmas, the mere embodiment of the good.
As a result, liberty ended up meaning «freedom» and «all men created equal» ended up «meaning» equality in the hands of demagogues that wanted to get the support of the plebs for their ambitions of power. This is the reason why suffrage got expanded more and more.
So now freedom and liberty are indistinguishable for everybody except some academics. Both the men in power and the men in the street thinks that USA is founded on freedom.
This is why the distinction between freedom and liberty is useful for the historian but I don’t think it is useful to describe the current situation.