In the United States, there are several different tiers of court. The state court handles a lot of disputes, particularly ones that relate to that specific state, rather than to the federal government. This means that state courts have a lot of work to do – most criminal and civil cases will be dealt with by them. Meanwhile, federal courts handle a narrower subset of courses.
In a state court, there is a trial court process to follow. The criminal case is filed, and if the case makes it to a trial then there is a hearing. Not all cases make it to a trial – usually there is a pre-trial, and in 90 percent of cases, there is a default judgement and that ends the case. In criminal cases, there are often plea bargains made before the case makes it to the trial.
State trials are held in a court that is located in the county street. If someone is unhappy with the decision that is made in one of the lower states, then they will have the option of appealing to an intermediate court, and then to the highest court in the state, which is named, in most cases, the State Supreme Court, and it will be located in the State Capital. There are higher courts, but it will take a long legal process to reach that.
The severity of the case is something that affects which court it is tried in. Minor offences are tried in inferior jurisdictions, while cases relating to rape, murder, or civil cases that involve large sums of money are handled at a higher jurisdiction.
In European courts, there is usually a separate court for serious crimes, but in the USA things are simply divided, in most cases, by the jurisdiction.