Enmity is a related term of spite.
As nouns the difference between enmity and spite
is that
enmity is the quality of being an enemy; hostile or unfriendly disposition while
spite is ill will or hatred toward another, accompanied with the disposition to irritate, annoy, or thwart; a desire to vex or injure; petty malice; grudge; rancor.
As a verb spite is
to treat maliciously; to try to injure or thwart.
As a preposition spite is
notwithstanding; despite.