To understand how the court systems work you need to know the flow of it all. Basically, the state courts usually always come first in minor, and major crimes. The only times when the Federal courts go to work is when the constitution is in question, or things like high treason, etc.
There are Circus Courts, District Courts, Appelate Courts, etc.
In the flow, both the Federal and State courts conjoin at the Supreme Court of the United States of America. I hope I'm right. If not, feel free to correct me!
Another answer you can give is that the interact by gathering evidence and convicting people. Almost all crimes our court cases start at a state level, so witnesses, juries, even the same plantiff will always be presented at a Federal Level.
