Is this your own informal categorization, or are you intending to rely on the meanings as used in political philosophy? Because this account of "unnatural rights" does not actually seem to square with the literature on the subject. (That is, just because something is an "unnatural" right, does not mean it is not a required right; it may be an optional thing, or it may be morally requisite for reasons unrelated to the inherent characteristics—i.e., not based on the "nature"—of the right-holder in question.)
If I may give my competing answer: "Rights" are moral/legal claims that should be respected, or else a penalty be suffered by the party that disrespects them. "Freedoms" are a specific type of rights, which protect the claimant from certain kinds of restrictions.
So the right to a speedy and fair trial is not a "freedom," because it has nothing to do with preventing restrictions on those who have it, but it is still a "right," because it demands a specific kind of action taken (by the government, in this case) toward whoever it applies to. Whereas "free speech" is a freedom, because it is specifically a right which forbids the government from restricting speech, except in certain limited circumstances (e.g. defamation or endangering public safety).