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.