The charges for murder vary by State. Here’s a New York lawyer explaining Murder 1 vs Murder 2 as it relates to New York State law. Murder 2 is regular premeditated murder. Murder 1 is murder with the intent of influencing or intimidating government ie. Terrorism. The lawyer in this interview suggests the Terrorism charge is, ironically, politically motivated, but it will be difficult to actually prove beyond a doubt that Luigi’s intentions were to change government policies and not just get even with someone he disliked.

In most places murder 1 is premeditated murder and murder 2 is manslaughter. Murder 1 in New York is different.

The jury makes a decision on both separately.
Charging with both gives the jury 2 options. If they don’t think it was premeditated and planned enough to convict on 1st degree, they can choose to convict on 2nd degree instead.

If the prosecution only charged him with 1st degree, the jury wouldn’t have any other option. And if acquitted on 1st, he couldn’t be tried again under 2nd degree.