New York Courts
The New York State Unified Court System is administered at the highest level by the Court of Appeals. Under this body, the NY Courts are sorted into ranks of descending level of legal weight, which constitute, first, the Intermediate Appellate New York State Courts, and after that, the New York Courts of Original instance. The latter begin the process of hearing cases, while the former have authority to hear appeals against decisions rendered toward them.
New York Supreme Court
The New York Supreme Court is not the main body of oversight and appellate functions over the New York State judicial system, as might be thought. Instead of this typical usage of the term Supreme Court, the New York State Supreme Court might be better compared to what are, in other State judicial systems, typically identified as district courts or circuit courts, thus possessing the power to originate trial proceedings as to legal matters.