There are many reasons why necromancy is lumped in with summoning Daedra or creating ethereal constructs under the "Conjuration" umbrella. A relevant one of them is that they all share a similar "scaffolding" nature, of creating spatially-bound structures that contain and focus magic. Daedra are given constructed magical bodies to inhabit; bound objects like conjured weapons are pure magic given solidity; and raised dead have an animating principle controlling them almost like puppets, almost directly manipulating their limbs.
This is not the full story, of course. Part of what makes necromancy appealing versus just summoning an ethereal construct or whatever is that it's possible to use the sort of muscle memory that gets embedded in the physical bodies of creatures to improve on direct puppeteering. Between a summoned construct and a raised corpse that are (under some given metrics) identically powerful and capable and smart, the raised corpse costs a lot less magicka and is much simpler to set up. The standardised reanimation spells all have simple ways of making use of the instincts of the dead to make them into more useful minions. So the main way in which these spells vary, really, is in how well they do this, how powerful and/or durable the raised creature is, and how long the spell can keep going before it consumes all remaining life energy in the corpses and turns them to dust.
Now, necromancy that affects souls can be much more powerful, because you're no longer constrained to the limited kind of intelligence that emerges from the combination of whatever is intrinsically programmed into the spell you cast and instincts and muscle memory. Reanimated ensouled dead are just people, kind of. People who are bound to the ones who raised them, and who live inside a body that no longer functions biologically and which is decaying more and more over time, but people. And the presence of a soul means they can use magic, which merely reanimated corpses cannot do. But overall it is terribly unethical to use, of course, since you are not only mind controlling someone but also preventing them from moving on to their afterlife.
(Kind of. It's not forbidden to do soul-affecting necromancy to, say, a chicken. Chickens don't go to afterlives. It's just that, since the techniques used to reanimate and reensoul a chicken are not distinct in kind from the techniques one would use for sapients, it is extremely frowned upon.)
Anyway all of this is to say that the very basic Raise Zombie spell that everyone learns almost as an afterthought at the College creates very weak, very stupid zombies. But the upside is that it is much faster to cast than the kinds of complicated reanimation spells these necromancers tend to prefer, and whenever one of them is taken down they become a weak zombie that will nevertheless be harassing their erstwhile friends from their own side.
It's horrible, actually, from a psychological and emotional perspective. Ruby frankly thinks he'd be traumatised if, say, Onmund died and immediately got raised as a mindless zombie to attack him, no matter how weak he was. He's not sure if these necromancers have built some kind of resilience to this but Ruby would not be okay if something like that happened to him.