Facebook has this week confirmed that it is now able to penalize false news and false headlines separately, after concerns that the two are not always connected.
As reported by Poynter:
"Now [Facebook] fact-checkers can either rate an entire story or just a headline as false, although the latter is demoted in News Feed less than the former."
The revision came up due to concerns around a specific case from last month, in which this article from Think Progress was marked as false and subsequently demoted in the News Feed.

In the article itself, Think Progress reports that, based on Kavanaugh's previous speeches, it could be implied that he would likely vote to overturn the abortion-rights decision Roe v Wade. But the headline, as you can see, clearly suggests that a more definitive conclusion.
The decision to downrank the entire article sparked a whole new debate about political censorship, and raised questions over Facebook's process on this front. In response, Facebook has added in the new measure - Facebook told Poynter that a false headline rating will not demote posts to the same degree as an outright false rating for an entire article, though it refused to give an estimate on the actual impact.
The clarification makes sense, particularly given that news publishers have become increasingly incentivized to use more divisive, attention-grabbing headlines in order to lure clicks.
With research suggesting that up to 80% of people will only ever read a headline when browsing online, publishers are able to spark discussion, and engagement (and thus, reach), simply by taking a more definitive angle on a piece - whether it's actually true or not.
For example:

As you can see, this post generated a heap of engagement - over 1,200 shares - while the majority of the more than 1,500 accompanying comments on the post relate to the dangers of spiders, with people sharing their personal experiences.
But the headline isn't true. White-tail spider bites are certainly not pleasant, but they don't generally lead to amputation - a fact which is clarified directly in the second sentence of the story.
"Doctors are now understood to be considering the more likely cause of Terry Pareja's illness to be a bacteria from Asia."
This is further underlined in the rest of the article.
"But Mr Pareja doesn't remember being bitten by a white-tailed spider, and even if he had been, it is unlikely its venom would have caused the necrosis, an expert says."
The man did lose a limb, and may have been bitten by a spider, but overall, the article is really about the mis-attribution of spider bites for such injuries. But had the publisher gone with the headline "Man loses legs to bacterial infection" there's no way it would have generated as much discussion and reach.
It stretches the truth, but it generates engagement, which is likely a significant contributor to the current divisions within society, that our media publications, driven by clicks, are, as noted, incentivized to present more emotive headlines.
This new measure from Facebook should help with this. By providing a way to penalize headlines, Facebook could lessen the benefit of such misrepresentations, which may reduce the publisher drive for such.
It takes work to assess content as its reported, so you can't expect Facebook to fix such issues overnight. But its another step in the right direction.