The distinction between spirits and corporeal undead notwithstanding, when creating undead, the difference between one and another will largely come down to what they can and cannot do—or even what they tend to be doing regardless of capabilities.
Speech and Other Sounds
In theory, a corporeal undead would have difficulty talking due to a tongue and more drying out. If a skeleton has nothing to talk with, spirits are even worse off. We may opt to ignore all of this so that they communicate effectively, or give them telepathy. Try to be consistent; if the undead walks funny, it should have trouble speaking clearly. It doesn’t make sense for one part of the body to be impaired but another to be unaffected by decay. If we want an undead to speak fluently but have trouble walking, we can fix this by having a leg wound cause the latter.
Completely silent undead or those making tormented attempts at communicating can be more frightening. An undead might be able to say only a few words, and if so, those are probably the ones associated with a goal. This could be the name of their child they want to save (or failed to save), for example. Another option is for it to emit a sound meant to draw others to it or affect them, such as causing a trance-like state in victims. Such a sound would make this undead type identifiable.
Touch
Corporeal undead have no trouble touching the world they’re still physically a part of, but does their touch corrupt in any way? It can be poisonous, infecting a limb that must be removed. It can just cause unbearable cold that lasts. We can decide it causes the person touched to have visions of what the undead sees, like who its master is, or what it wants, or what horror it faces now. These results and others of our invention can be part of our undead type.
Since disembodied spirits don’t inhabit a body, by definition, it’s logical that their ability to interact with the physical world is compromised, and yet we’ve all seen movies where they can move objects or directly touch the living. Sometimes this touch is something they must learn or which takes a toll on them to perform; otherwise it’s too easy and they don’t have limits on their powers.
Decide how much our spirit can manipulate the physical world, how often, for how long, and to what end. Are they only able to pass through some kinds of objects and not others? Does the material something is made of affect their ability to touch it? Are they only hurt by something like silver? Can they touch people and if so, what affect does that have on the living or the spirit?
The ultimate version of touch is possession of a victim’s body. An appealing idea involves the victim gaining the inhabiting spirit’s skills—becoming an expert musician or gymnast, for example. A caveat here is that the body won’t have the training. The body simply wouldn’t be capable of it, but this again depends on how realistic we want to be.
Movement
The slow-moving undead of yesteryear seemingly paid more attention to realism but has given way to faster-than-humanly-possible corporeal undead. Assuming we want to justify anything, the latter can have either a supernatural, technological, or possibly genetic cause (in the form of mutation). Slow moving ones don’t seem frightening anymore unless sheer numbers have blocked escape routes. Today’s audiences expect better than victims who just stare in horror until undead surround them.
If we’re giving our undead superhuman abilities, a good rationale sells this better. Knowing their origins will help; if a spell designed to grant speed to someone killed them instead, then making them fast in death makes sense. An animated corpse is presumably powered by unholy forces that also allow it to experience little or no fatigue.
Spirits are often shown gliding around or just appearing as if teleporting; the latter suggests knowing they’re dead while the former suggests ignorance of this fact. Can spirits pass through objects? If so, this can be because they don’t recognize a change has taken place, such as a bookcase being placed in front of a door long after they’re dead; doing so might not indicate awareness of their death but being stuck in time, seeing the past instead of the present.