What Is the Definition of "high Federalists"?

According to SparkNotes, the High Federalists were a branch of the Federalist political party that emerged due to differences in the ideologies of John Adams and Alexander Hamilton. This division of the Federalist party led to its decline.

The High Federalists emerged around 1795, with John Adams' election to the presidency and Alexander Hamilton's resignation from the Treasury. All Federalists were in favor of a national bank and strong central government. High Federalists, however, sided with Hamilton over Adams by calling for war with France, and they officially broke from the Federalist party when Adams refused. The Federalist defeat in the presidential election of 1800 and the subsequent decline of the party is attributed to this major party division.