As always with these, you should take a look at source materials to get an idea of how things are written in canon. A good source for this particular topic is the Libris Mortis, which you can probably find somewhere on the internet.
However, I'll still break these down with some estimations of how I thought they might work from an IC standpoint while I was developing the Streams. These are by no means an absolute guide and you should take it as inspiration more than anything else.
Zombie Stream:
Animated, mindless undead. No soul is retained. You can either animate them on the spot or summon some pre-animated ones. Though some differences exist where the undead may try to form words.
Skeleton Stream: Many skeletons might be instilled with enough intelligence to speak, but they are often only used for simple tasks and are simply incapable of doing anything overly complex. They are not instilled with a soul, but some necromancers might try to put a soul into a skeleton if they're ambitious enough. The result is rarely what they desire, though, and these creatures are often unable to cope with their circumstance.
Ghoul Stream:
Ghouls are creatures who have been twisted into undead carrion feeders that often feed on the flesh of the dead, they're generally trying to kill and then eat but not always. These are not animated. They retain very few similarities to who they were in life, and they are not completely mindless, but the soul is twisted if not entirely gone. You are usually summoning these from somewhere else after they are already created. Abyssal ghouls especially normally come from the Abyss and are said to be those ghouls who succumbed to the influence of Orcus, or were changed by it. Orcus might gift these to a necromancer in their service, or to someone who asks if he's feeling generous.
Mummies:
These are always created by burial rites which are often in tandem with either a curse (either intentional or ambient) or they are placed as guardians in many tombs, especially Mulhorand and Sibayad. These creatures remain wise and intelligent all the way through their eternal unlife but they are altered by the nature of their creation. There is much debate whether the soul is retained in a mummy but many lean towards "yes", and that these types of undead in fact are never allowed to leave the mortal plane that they are charged to protect, though it could go either way. You're always summoning these but there's room for flavor like a cursed item or a charge of post-mortem service or something they might react to and choose to make you the subject of their protection and service
Vampires:
Always created through either the vampiric curse or perhaps a rare few circumstances, such as unholy intervention or some rare cursed items (I once played a character who turned into a vampire because they drank from a cursed chalice). These are never mindless and in fact very intelligent, and they are often difficult to tell apart from who they were in life, but the soul has been twisted into the creature they've become or is completely gone entirely. I think the debate about it is what makes this type of undead fun to respond to. I thought these to either be summoned, or if summoned by vampires, can be roleplayed as childer. In many cases, characters make blood treaties with existing vampire clans to use their services, too.
Ghost Stream:
Always sentient. You might notice that not all of them are evil, either; the weaker ghosts are typically True Neutral. This is because a fresh ghost created by unfinished business is not necessarily malign, and is very similar to who they were in life, as their soul is not yet twisted. Some ghosts are created through the touch of evil or through intentional necromancy, and many of these are either tortured beings or outright evil. As you progress through levels, you'll notice that the ghosts gradually shift in alignment towards evil. That is because many ghosts, over time, lose more and more of their selves, and the capstones are not even regular ghosts anymore, but Banshees, who are always evil. You're summoning these always, but I suppose there's possibilities in creating them yourself if you know how to.
Wight Stream:
These are tricky because the capstone undead is not even a wight, but a Revenant. There was a reason I put it in there, though. Most wights are undead who are twisted into evil by sheer hatred and violence, and so their souls likewise become an abomination of what they originally were. I don't believe wights lose their souls completely, merely that they may be replaced by the new creature they become. Revenants, though, are something a little different. Revenants are created through a similar process, they die, there is hatred and violence, and then there is a will to rise from the grave to get revenge upon whoever slighted them.
The issue with this as a necromancer, though, is that you yourself are unlikely to be that person; the revenant would try to kill you, but if you were proficiently powerful enough, you could likely control any revenant and turn it to your side, though it would loathe you for stopping it in its task, lest you assisted it in completed it (before finally dismissing it). Wights on the other hand are always summoned, but I think necromancers of proficient skill could create them.
Abomination Stream:
These are constructed dead. Skilled and even amateur necromancers can put these together from a variety of corpse matter and bring them to life with animation. They often retain little of who they were in life and are usually very mindless, not sentient at all, and directed in the manner of any other construct that does not think for itself. HOWEVER… you could make a case that they might have a personality, and their personality might be a combined, tortured amalgamation of all the different people whose appendages and body parts were used in their construction (imagine how nightmarish that would be). I wouldn't discourage anyone from trying to say that an abomination was intended to be sentient by its creator, nor would I say that it's impossible. However, in many circumstances, if you look at the character sheet, they are very low intelligence and wisdom. This means that generally they weren't intended to be conscious of what they are. I know that the staff, though, doesn't make a habit of punishing players for creativity.
Beast Revenant:
I've had tangents about this one. Although many Beast Revenants were once animals (who only had a certain measure of sentience/self-awareness to begin with), Beast Revenants are no longer what they originally were (aside from the Wraith Spider, which is a canon undead creature and kind of differs from the rest of the undead in this Stream). In short, Beast Revenants typically begin life as normal animals but are then warped by cataclysmic uses of necromantic power or ambient fields of negative energy left behind in the wake of exceptionally powerful necromancy spells. You could make a case for curses, too. The most known cases of beast revenants being created are actually that of Necromantic Torture, where someone who is experimenting with necromantic power uses it to torture an animal to death. The animal is killed and their spirit becomes trapped. Over time, the result is a warped creature that, though once not aware of much at all, now BECOMES aware of what happened to it, its new state as an undead creature, and even (in many cases) the reason they are what they are. This instills in the otherwise innocent animal a preternatural hatred for all life and an evil that can only be quenched by becoming the hunter.
Wraith Stream:
Wraiths are an undead creature born of evil and darkness, despising light and all living things. They drain the life from living creatures, turning them into new wraiths upon death. Wraiths are an incorporeal Stream that barely retains anything from what they were in life, and are typically not interested in anything except the destruction of living matter and the snuffing of light. These are typically summoned from the Negative Energy Plane where many wraiths make their dwelling. Though wraiths are typically intelligent enough to pursue their aims, they are not usually scheming creatures. They're rather automatic and grounded in repetition at times.
Drowned Stream:
There's actually some variance with these. In some cases, the drowned dead are summoned from the depths of the seas and animated by their necromancers. In other cases, they are called to arms by whoever holds occult power over their original crew (such as Davy Jones and the Flying Dutchman) or perhaps are even in a pact to man the ship they were scuttled down with. There's always room for curses like in The Curse of the Black Pearl, too. Their mindlessness and intelligence are meant to range from completely nonexistent, to actually not that much less, and some Drowned Dead might not be that much different from who they were in life. It's important to know that these creatures are almost always evil because of what unlife does to you, though, and while some drowned dead might behave as they were in life, it's more likely they are simply "stuck on repeat": sailing, pillaging, killing, and doing all the things they did as living creatures. Mind you, Drowned Dead can also be sailors who weren't pirates, but typically they are depicted that way in the game because I didn't feel inclined to create even more options (when there are already so many) and we all know that Dread Pirates are probably overall a more sensible (and cooler) generic option for the capstone undead.