Actually, that isn’t true in this case (or in the 1968 law that that this amends).
Under normal circumstances, most crimes are state crimes; there’s no federal jurisdiction. If you were to come over to my apartment and I kill you, then under normal circumstances. I haven’t committed a federal crime. I’ve committed a state crime, and I can and will be arrested by Virginia, but as far as the federal government is concerned, I’m all good.
What you saw happen in the 50s and 60s, though, in parts of the South, is that certain state crimes weren’t being prosecuted in those cases where the victims were black and trying to exercise their civil rights. People were being lynched because they were organizing voter drives, they were being assaulted because they were going to desegregated schools, and so on. And there wasn’t anything the federal government could do about it, because murder and assault and vandalism and so on weren’t illegal under federal law.
So, in 1968, after the assassination of Martin Luther King, Congress passed a law that made it a federal crime to commit a crime against someone based on their race, color, religion or national origin in order to keep that person from exercising a federal right. That way, in the event that a state wouldn’t prosecute a crime like this, the federal government could.
What this change to the law does, is first, extend federal protection to gender, sexual identity, gender identity, and disability, and second, to remove the restriction that the crime has to have been committed to keep the victim from exercising a federal right.
So in this case, this hate crimes law isn’t just a sentencing issue. 45 states have their own hate crimes laws, and those are predominantly laws that enhance sentencing.