decision
majority opinion
Opinion of the court.
Depending on the context, it is usually a verdict, a ruling, or a holding.
Dissent
Majority opinion
Majority opinion
Majority opinion
Majority opinion
The written explanation for the US Supreme Court's decision is called an opinion.See Related Questions for an expanded explanation.
A ruling priest is called a Theocrat
It is called the same. Other than a public ruling, which affects the relations of state governmental bodies, private ruling deals with private persons, which can be an individual or an entity, whether business or not.
The detailed explanation is called "the opinion of the court." In it, the court typically sets forth the facts of the case, then sets out the law that applies, then applies the facts to the law and comes to a conclusion. It then enters an order or judgment consistent with the opinion.