As far as I am aware, the idea of neuromodulator comes from the fact,
that early electrophysiologists, could see classical, fast, synaptic
transmission, mediated by glutamate, gaba and glycine etc, working on
ligand gated ion channels to rapidly modulate resting membrane
potential. But neuromodulators, like dopamine, serotonin or histamine
didn't have these same kind of actions. They might decrease the release
of the classical fast synaptic neurotransmitters, or enhance them.
The differentiation between neurotransmitters and neuromodulators isn't
as common anymore, and I certainly don't encourage it, as a
neurotransmitter can also act like a neuromodulator (GABA working on
GABA-A and GABA-B receptors).
Most "neuromodulators" are released in the exact same fashion as
neurotransmitters, (calcium influx caused by the action potential,
leading to neurotransmitter release), though there are some exceptions.
The have effects of ion channels and gene transcription. On short term,
there effects are mediated through kinases and other intracellular
messengers, leading to alterations in membrane resistance, resting
potential and calcium flux.
This is a pretty simplistic view, but it serves most purposes