Necromancers can use the ashes of the dead to allow them to see and control ghosts, to animate and control dead bodies, to seal spirits in objects (including bodies), to make themselves and others undying, to resurrect people, and various other death-related effects.
Rituals to do this involve drawing precisely and/or intuitively with ashes.

Nekyia are born with an excess of regenerating necromantic energy which lets them perform necromantic acts at will, though the use of ash diagrams and chants will lend them better control.
[Diagram-Makers] instinctively know how to make working necromantic ash diagrams, though it takes practice to get good at closing loopholes. You can become one through a ritual, but it's a very complicated one which has been lost over and over again. Most are born with the talent.
Mediums are born able to see and to some extent interact with ghosts, and can invite them into their bodies without a ritual to do so. This can also be done using necromantic rituals, and in fact the creation of born mediums was a ritual in the first place.
Necromancers are anyone who uses necromantic magic, including all nekyia, but technically not including mediums who don't otherwise perform necromancy.
Necromantic power is power gained from death. Nekyia are sometimes born when they were exposed to a lot of death while in the womb and acquired a tear between the realm of life and death as a result.

Ghosts vs Spirits: Ghosts are around just a step away from the living world, have necromantic energy of their own (which they produce and can gather from sites of death), can haunt people, with enough energy can affect the living world, and cannot refuse a summon from a working necromantic ash-diagram. The vast majority of them do not have much necromantic power, many of them not even enough to properly hold a human form.
Spirits are in ~The Other Side~, enjoying the afterlife (which is sort of... floating in everlasting bliss) and waiting for reincarnation. They can refuse summonses if they wish - and plenty of older ones will - and have no necromantic energy of their own (though once they're summoned out of the other side they can be left out long enough to become ghosts).