Your question is incredibly unclear and it is hard to say what you are really getting at.
The big divisions in the U.S. in terms of types law are based largely upon the remedies available in each type of litigation (and it is more useful to think of litigation as a means of legal rights enforcement or requests for justice to be done, rather than in the popular vernacular in the profession as "dispute resolution" forums).
Criminal law, where the consequences include incarceration and non-compensatory fines, but compensation for victims is limited to restitution which is often quite grudging. The cases are brought by the People (basically, the government) against someone who has violated a particular criminal statute.
Civil litigation at law, where the consequences typically involve an award of compensatory money damages, punitive damages proportional to the compensatory damages, or possession or ownership of particular items of property, and there is a right to a jury trial. These are lawsuits brought by one person against another. Debt collection cases, personal injury cases, evictions, repossessions, and sometimes foreclosures of legal mortgages are included in this category.
Civil litigation in equity, where judges can issue orders telling someone to do something or not do something, which are called injunctions, can dissolve or form legal relationships like divorces and guardianships, in which there is no right to a jury trial. These are lawsuits brought by one person against another, and also situations that require court intervention even in the absence of wrongdoing or disputes (like the appointment of a guardian for a minor child) in situations that mainly involve private parties.
Administrative law, where a government agency's treatment of someone or grant of a privilege or regulation is at issue, such as driver's license revocation hearings, deportation proceedings, real property zoning change requests, environmental regulation notice and comment in advance of regulations issuing, etc. A key subset of this is tax law. These pit the government against a private party, or two people disputing what the government should do disputing each other with the government either taking sides or taking its own way or not offering an opinion. They typically start outside the court system but are subject to judicial review by the courts.
The reality is messier than that, so law and equity issues, for example, may be tried in the same case, but those are the main divisions of U.S. law and are mostly based upon the types of remedies available. Sometimes all of these kinds of law will be handled in a single court, but the procedures that apply to each kind of case vary.