Jury cases are either civil or criminal. Civil cases are disputes between private citizens or institutions such as corporations. Generally, the party that brings the suit is requesting that the Court award damages for the harm suffered.
A criminal case is a lawsuit brought by the State against a person who has broken a criminal law. Most criminal cases are tried by a judge in the presence of a jury, and may result in sentences under criminal law. Such sentences could include jail time as well as fines.