Lawsuit Information Center
The United States uses a federalist system of government. This allows each of the fifty states to be fairly autonomous and limits the amount of power that the federal government possesses. One of 
the consequences of having this type of system is that there are state entities and federal entities. Courts are a prime example. There are both federal and state courts, so it is important to have a grasp of their respective purposes and powers.
Purpose of State Courts
Courts have to have jurisdiction in order to make rulings and decisions. The reason we have so many different state courts is because each court has a fairly limited jurisdiction. A county court in Maryland cannot have jurisdiction over something that took place in California. That is why courts are closely tied to geographical territory and why most of their power extends to people or occurrences that take place within that territory.
This being the case, state courts have the power to enforce the laws of the state where they sit. Given how my firm is centrally located in Maryland, let us use that as an example. The trial courts of Maryland have the ability to adjudicate cases involving the laws of Maryland. For example, these courts have the ability to adjudicate cases involving violations of Maryland’s criminal law. Speeding tickets, assaults, robberies, and thefts are all examples of things that Maryland lawmakers have made illegal. Thus, it is up to the state courts to apply that law considering it is within their power.
The same goes for civil cases. State courts (generally) have the ability to resolve disputes between citizens of the state or for matters that occurred within a state. States also enact certain civil laws, which State courts have jurisdiction over as well. And of course, each state has its own common law, or judge-made law, which is applied by state judges.
Federal Courts
Again, our country relies on federalism to operate, meaning there are both state governments and a federal government. And just as the state government passes laws, the federal government does so as well. So when an issue comes up that involves federal law, federal courts are the ones that are responsible for hearing and adjudicating those cases. For example, a dispute involving a federal act, such as the Affordable Care Act, would be adjudicated in federal court. Considering how the states did not have their hand in passing the Affordable Care Act, it would not make sense to allow state courts to make determinations regarding the Act. At the same time, federal courts are responsible for hearing cases that deal with the federal Constitution. So should a case implicate a Constitutional provision, the proper venue would be the federal courts. This is what is known as federal question jurisdiction.
You may have noticed a “jurisdiction gap” above when I discussed state courts. What if someone who lives in one state sues a resident of another state? Depending on how much money is at issue, the case could potentially end up in federal court. The doctrine of diversity jurisdiction allows a plaintiff to bring suit in federal court even though the case may involve issues of state law or is just a standard lawsuit involving residents of different states. Diversity jurisdiction protects against home-field advantage. Just as the Baltimore Ravens tend to play better at M&T Bank Stadium, parties to a case tend to be more successful — and feel more confident — in their home state courts. Federal courts are a more neutral tribunal because they often will not have as significant a stake in the matter. This is true now but I’m sure it was particularly true in 1801. So diversity jurisdiction allows a federal court with proper jurisdiction to hear the case.
Diversity jurisdiction is not something that was inherent in the power of federal courts either. This type of jurisdiction was created by the federal government back in the day to make sure litigants were getting a fair shake. It is one of the key differences between state and federal courts. At the end of the day though, keeping track of the difference between state and federal courts really only involves keeping federalism in mind. State law, issues, and citizens equals state court, while federal law and diversity jurisdiction equals federal court.