In the US, you have two kinds of legal cases: civil and criminal. A criminal case is that the government is charging you for a crime, and there are various levels of intensity, such as if it is a state or federal crime, if it is a misdemeanor or felony, ect. If you have been accused of a crime and either refuse to show up to court or avoid arrest, the government can issue a warrant for you, which is essentially a document that allows police or similar figures to freely arrest and haul you to court for avoiding justice. Also, in a criminal case, the people who are trying to prove you committed a crime are called the prosecution.
A civil case is entirely different in that it is a civilian accusing another civilian of causing some form of harm. It isn't always person on person, sometimes it's companies vs a person, or a person vs a company, ect. The point stands that a civil case is meant to resolve a dispute between two parties, not to find someone guilty of a crime. Civil cases could see one person seeking payment for lost wages, or restrict someone from contacting you, or make someone stop spreading lies about you, ect. The one who begins a lawsuit is a plaintiff, while the one being sued is the defendant.