Not to be too blunt, but the difference between the two seems obvious (of course that doesn't mean you have to agree with the law's treatment of that difference): Libel has the potential (and I think, by definition, the intent) to have concrete harmful consequences, while US-flag-burning is purely expressive - the harm is only emotional (if we assume the burning is done safely, since that's irrelevant to the topic).

Maybe you could argue that it "encourages" further action and should be covered under something similar to hate speech laws, but it doesn't seem specific/actionable enough to make sense - and anyway, that's tangential to the question of the difference between libel and US-flag-burning.