Indeed it is. It is the difference between premeditated murder and voluntary manslaughter. It’s also referred to as a crime of passion, or “in the heat of the moment” killing. The classic example is catching your spouse in bed with someone else, and then killing your spouse and/or the other person. Common Law recognizes these circumstances as meaning that the killer is, legally, not entirely in control of themselves in the moment, and so can’t have the required mens rea (intent) to satisfy the definition of 1st degree murder.
Source: manslaughter | Wex | US Law | LII / Legal Information Institute
ETA: Also, importantly, you can’t have had time to cool off from the provoking incident. And, in my opinion, finding out a judge was sexually abusing your minor daughter would qualify as such provocation. But if the sheriff had found out about it the day before, then he had time to cool off, as far as the law is concerned, and this would be first degree murder. But if he found out right in the moment, when he was looking at the judge’s phone, then that’s probably voluntary manslaughter. Lastly, it doesn’t actually have to be true that the judge was abusing the sheriff’s daughter. The sheriff would just have to reasonably believe that that the sheriff was doing that.
