And yet different states have different definitions of what constitutes "murder" and differing penalties. We don't have a federal law against murder, yet amazingly enough it's pretty rare.
1. All states recognize murder as a crime.
2. We do have many federal laws against murder. Check US Code Chapter 51. At that, section 1111 federally defines the classifications of murder (1st degree, 2nd degree and so on..) States are just the ones who enforce this in most cases but the law is federal.