As adjectives the difference between large and higher
is that
large is of considerable or relatively great size or extent while
higher is (
high).
As nouns the difference between large and higher
is that
large is (music|obsolete) an old musical note, equal to two longas, four breves, or eight semibreves while
higher is a national school-leaving examination and university entrance qualification.
As an adverb higher is
.