Edit: I forgot, intention to commit a felony carries premeditation, so it would even be attempted first degree murder
My understanding was that murder required premeditation, and intent to kill without premeditation was manslaughter.
Intent to harm without intent to kill typically corresponds to (voluntary) manslaughter. Reckless disregard or negligence of the potential for death may result in manslaughter or some lesser charge like involuntary manslaughter.
This differs by state; some have crimes like "3rd degree murder" or "2nd degree manslaughter", or "voluntary manslaughter" vs. "involuntary manslaughter".
There are also delightful variations where someone "sufficiently provoked" (adultery being the traditional example) would face manslaughter charges for what would otherwise be murder.
This isn't as true as you make it seem