Why did the Federalists divide among themselves into high and moderate Federalists during the 1796 presidential election?
The High Federalists were what we might call today the "extremist" wing of the party. This was the part of the party that believed most strongly in its ideology of a strong central government that would be active in promoting economic growth. This was also the part of the party that most wanted to go to war with France.
The split between the two occurred largely because of disagreements between the extremists and the moderate Federalists over the idea of war with France. The High Federalist extremists felt that a war with France was necessary while the moderate Federalists did not. This led to a split within the party.