"High Court" is "Supreme Court in the USA, right? In the UK, it is different?

From Wikipedia:

"Her Majesty's High Court of Justice in England (usually known as the High Court of Justice of England and Wales, the High Court of Justice or, simply, the High Court) is, together with the Court of Appeal and the Crown Court, one of the Senior Courts of England and Wales. Its name is abbreviated as EWHC for legal citation purposes."