In the context such as "free press", it means libre from censorship, "gluten-free" means libre from gluten and so on. Then there is "free stuff", why is the same word used?
If so, my analysis amounts to a rule in search of actual usage—a prescription rather than a description. In any event, the impressive rise of "free of" against "free from" over the past 100 years suggests that the English-speaking world has become more receptive to using "free of" in place of "free from" during that period.
"Free of" vs. "Free from" - English Language & Usage Stack Exchange
Free ride dates back to 1880, while free loader is a more recent construction “freeloader (n.) also free-loader, by 1939, from free (adj.) + agent noun from load (v.)As a verb, freeload is attested by 1967 and probably is a back-formation from this”
Similarly, “free education” is funded by the state (which is ultimately financed by taxpayers) and taught in state-run schools called state schools whereas schools that charge tuition fees are termed private schools. A private school in the US typically means fee-taking. Confusingly, in the UK, they are known as public schools.
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I don't think there's any difference in meaning, although "free of charges" is much less common than "free of charge". Regarding your second question about context: given that English normally likes to adopt the shortest phrasing possible, the longer form "free of charge" can be used as a means of drawing attention to the lack of demand for ...
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