This article might give a clearer idea of what @Knights_Mom is talking about?
https://www.nolo.com/legal-encyclopedia/what-lesser-included-offense.html
The Elements Test
But the most popular approach to identifying lesser included offenses among courts is the elements test. Crimes consist of elements, like a recipe consists of ingredients. Someone who commits each and every element of a crime has committed the crime. The elements test doesn’t look at the charging document or the evidence. Instead, it considers only the definitions of the crimes standing on their own.
This test provides that a more serious crime contains all the elements of a lesser included crime, plus one or more other elements. Under this test, regardless of the pleadings or the evidence, assault with a deadly weapon is not a lesser included offense of murder. That’s because the definition of murder doesn’t require that the killing occur through use of a deadly weapon. (Hoffheimer, supra .)
I’m not familiar with the NJ statutes, either, but whether or not assault with a deadly weapon could be an included lesser offense depends on the NJ definitions and on if the elements test applies. This could be the reason that assault wasn’t charged.