The main types of Apparition Encounters that I personally give real interest to are the ones with Veridical Details associated with them. (That is, Verifiable Details.) The types that highly suggest there may be more going on than mere hallucinations and "just seeing things". Simply "Seeing An Apparition" isn't very convincing (unless multiple people witness it at the same time and describe the same entity, of which there are many cases, kind of hard for multiple people to hallucinate the same detailed entity) and can easily be explained by hallucination or the eyes playing tricks on you or a similar explanation, save for those types of cases with Veridical Details being imparted from the encounter, those are far more interesting, but are still largely subjective accounts. You can't generally measure or reproduce on demand these anomalist encounters, as they are by their very nature, anomalist, but they are very intriguing.
Veridical Types of Apparition Hauntings...
* Veridical information revealed to the witness/witnesses either in the apparition's appearance (such as specific clothing, facial/body features, injuries, etc), movements (such as having a distinct limp), smells (such as the distinct smell of specific lady's perfume that the person wore in life and no one else in the household owns or keeps), the specific location (such as the apparition being spotted in the place of death or great tragedy), or relayed veridical information that is later verified as factual about the deceased (such as later matching their description with an old photograph of the deceased, or being told who killed them, the location of valuables, or specific phrases known being uttered which matches their personality known only to living relatives/friends).
* Especially interesting are the cases where multiple people, either together at the same time, or independently at another time at the same location, end up describing the *exact same entities* they are witnessing. Even if they had no prior knowledge of the location or it's history.
Now, another type of Veridical Apparition Encounter is the Phenomenon known as After Death Communication (ADC)...
* A classic example are the cases where the apparition of a relative who is known to be in good health appears to a loved one, totally unexpected, and either announces their death or fades away without speaking, all when the experiencer was in good mind and not stressed, and later that day or the next morning, the experiencer finds out that the same relative died unexpectedly the night before or earlier in the day, shortly before they were visited.
* If the apparition is unknown to the person, there are many cases where the apparition was identified by other means: The apparition wears specific very unique clothing, has a unique scar or birthmark or is injured or bandaged in a certain way, a very unique hair style, has a distinct limp, smiles in a certain way, or some other physial characteristic that is later identifies them when the witness or witnesses speaks to other people / relatives / friends, or sees them in a photograph.
* The witness or witnesses may be visited by an apparition and believes them to be a living person, because unknown to the witness, the person had actually died sometime before, and the witness or witnesses was not aware of it.
* The apparition either directly tells them or shows them something important (a family secret, a lost will, how they died, who killed them, etc) that is later independently verifed to be true.
Then there is the Phenomenon known as Death Bed Visions (DBVs) where a person near death witnesses deceased relatives surrounding their death bed waiting on them. This is signifcant for the Veridical Details in many cases.
Death Bed Visions often contain Veridical Elements such as the following...
* Visions seen by the Dying of Persons *unknown* by them to be Dead, but known to the Family to be Dead. (Such as a younger relative who may have died in a car accident during the dying person's illness, that the family decided not to tell them about in fear it would make them more ill, and just before they die, they are shocked to see this young person's spirit waiting on them, calling on them.)
* Visions seen by the Dying of Persons *unknown* by them to be Dead, and likewise *unknown* to the Family to be Dead. (Such as a relative who unexpectedly died hours or days or weeks before, but news had not yet reached the family of their demise, and the entire family assumed them to be alive, yet the dying person sees them waiting on them as a deceased family member, which is later confirmed.)
* Visions seen by the Dying of Persons Known by them to be Dead, and Death-Bed Visions seen by others. (Sometimes, even the visions of the dying of persons known to them to be dead contain Veridical Elements, such as the dying seeing them wearing certain clothing or certain accesories they had earlier in life that they had never seen them wear personally, that is confirmed by other family members who would have known. And in some cases, people not close to dying have seen spirits of the deceased waiting on the dying person before their death, didn't know who they were, later described them to other relatives, and found out who they were.)
The above types of Veridical Encounters highly suggest that certain Apparition Phenomenon is more than simply "hallucinations" or "just seeing things" when you examine that many of them contain strong veridical elements aside from merely "seeing a ghost". That's the interesting part. However, proof, as in absolute end-all proof, is harder to come by, as these are subjective experiences. But are very interesting regardless.