Confusing fact of the day: Trump's trial today was in NY County Supreme Court. Unlike in the federal system and most other states, in NY state the main trial court for most large civil cases and felonies is called a "Supreme Court". Each county has one. ("NY County" is Manhattan). The final appellate court of last resort in NY state is called the "Court of Appeals" (the NY State equivalent of the US Supreme Court).
Yes, this is confusing.
NY City seems to go especially out of its way to be confusing about stuff. In addition to its "Supreme Courts" being where regular trials are held, the City of New York consists of five counties, one for each borough. But only the Bronx and Queens have county names that are the same as the borough names; Manhattan's county is "New York", Brooklyn's is "Kings", and Staten Island's is "Richmond". And the BOROUGH of Manhattan isn't quite the same as the ISLAND of Manhattan.