Multiple Rehearings and Appeals of a Court Decision
Many jurisdictions have two levels of appeals. For example, if a case is brought in the general state trial court or court of records (known as the "Superior Court" or "District Court" or "County Court" in most states, but called the "Supreme Court" in New York) there may be one set of appeals from the trial court to an intermediate appellate court (most often aptly named the "Court of Appeals" but in New York, the "Appellate Division of the Supreme Court").
The losing party may then take a second appeal to the highest appellate court in the state (typically known as the "Supreme Court" but in New York, as the "Court of Appeals", and in Massachusetts as the "Supreme Judicial Court"). In states with more than one level of appeals courts, the highest court can refuse to hear most cases, in which event the decision of the intermediate level appeals court is the last word and the case is over.
If a "federal issue" is involved, sometimes there will be what the media terms an "appeal" from a state's highest court to the Supreme Court of the United States, but this review is usually obtained when the Supreme Court grants a "Petition for Certiorari", discussed later.