More correctly its called "Federalism" the idea that some powers are given to the national government, while others are reserved for the states. Who gets what powers has lead to about 200+ years of arguing and a very bloody Civil War.
If you are found guilty of a state crime, you go to a state pen, if you are guilty of a federal crime, you do federal time. The differences are huge. First off, there is no parole, or time off for good behavior in the federal system, and though many federal prisons are called 'country clubs' others like the Super-Max in Colorado or the one in Marion Ill. are pretty foreboding.
Other areas are still touchy, gun laws (some states like New York, its all but impossible to get one, other states, you can walk in off the streets and walk out with an arsenal. Drug laws are another, in Texas, which seems to be the running example, The possession of up to a pound of marijuana (this includes very minor amounts) will generally carry a sentence of 6 months to 2 years in a state jail and a $2,000 - $10,000 fine. Other places, have decriminalized small amount, other have open marijuana sales if you have a medical card. Card or no, its all but impossible to get busted for puffing in SF unless you blow the smoke in the cops face, and even then...
So, a lot depends on where you are, what you are charged with (and you are not going to walk easy on any sex charge that involves a minor anywhere) and, of course, how good your lawyer is.
And, I think you are referring to the case of Christie Lee Cavazos Littleton.