Most US states have:
Capital murder - murder in conjunction with rape, robbery or kidnap and, in some states, murder of a law enforcement officer or fire/ambulance/SAR personnel and/or murder of a child under a certain age.
In some states, this is punishable by death, in orders, by life imprisonment without the possibility of parole.
1st degree murder - must prove premeditation
2nd degree murder - varies by state
voluntary manslaughter - something like this if the baby had died.
involuntary manslaughter
death by dangerous/reckless/careless driving and/or known as vehicular homicide - self-explanatory
Then various forms of assault.
Most cases are handled in state court, in which case you hear it as The State of X v. Defendant X.
Some are federal, in which case the case will be The U.S. Government v. Defendant X. Federal crimes take place when a person commits a crime in the course of crossing a state border, a crime against a federal officer or in a federal building, a crime crossing state lines such as drug trafficking or treason.