At the risk of, as my colleagues may put it, “copping out,” that’s actually a mystery. While scientists have had plenty of verified psychics who were willing to submit to testing (Sabrina, for example), the truth of the matter is we don’t entirely know how their abilities work.
We do know that these abilities are wilder than a pokémon’s. That is, while a pokémon’s abilities may take specific forms (Psychic is still a very specific technique with a very specific “look,” regardless of its source), the telekinesis wielded by humans tends to be less uniform. That is to say, even though such abilities will always do one specific general thing, how powerful that thing is or its “rules” vary from subject to subject. For example, Sabrina’s psychic abilities are so powerful she can actually use them to trigger a transformation into a subject or to astral project part of her own soul into a tangible, childlike version of herself. A psychic using the same abilities (identified as telekinesis and astral projection) might only be able to manifest a spectral form of themselves or bend an object. Still others may only be able to use telekinesis to lift and move objects. It’s still absolutely the same ability—just in different forms. Moreover, although most if not all humans possess either mild or latent abilities themselves (or at least they do according to popular theory), which abilities again depends on the subject. Some human psychics exhibit no telekinetic talent whatsoever but possess instead psychometry or clairvoyance.
All of this is to say that how psychic abilities work for humans isn’t much like how it works for pokémon. While pokémon abilities are also not well-understood (the going theory is that pokémon have differently developed brains than we do, hence their ability to use extrasensory talents), there’s no real reason why members of our species would display vastly different abilities of wildly different levels of strength, with each ability manifesting in completely different ways. It would be like a Thunderbolt varying from pikachu to pikachu. Certainly, there are some pikachu stronger than others, but a Thunderbolt is still recognizably a Thunderbolt. Moreover, every pikachu can still learn Thunderbolt; it’s not as if only certain pikachu can learn it while others can control fire. Or in other words, yes, pokémon abilities and human ESP are very much different breeds of abilities.
As for the others, as a disclaimer, mediumship is considered a type of ESP. It’s simply communing with the minds of the deceased, rather than the minds of the living, and oftentimes, mediums display other forms of ESP on top of their ability to tap into the spiritual realm. Aura users, however, are considered to be completely different things, as their source of power comes not from the mind but instead their own life force. While it’s true that they can control this life force mentally (meaning some may argue that it’s yet another form of ESP), it’s still more of a full-body action akin to the difference between psychic- and fighting-type pokémon, if that makes sense. These are also not the only abilities humans are known to possess that almost mirror pokémon ones. There are documented cases of pyro-, hydro-, and even geokinesis among humans, and it’s said that historical examples of witchcraft might have actually been the manifestation of abilities similar to fairy-type pokémon. It’s even thought that the ability to understand pokémon as if they’re speaking Common can also be categorized alongside the aforementioned.
But for how vastly different these abilities are, pokémon abilities and human abilities (of all kinds) supposedly share one important detail: their origins. As you likely know, there are stories in Sinnohan folklore that claim that humans were once closer to pokémon than they are now. While it’s unlikely that we were literally the same species (we’re too genetically different for that), it is likely that the abilities we have may have come from the same adaptive path that gave pokémon their abilities. That is to say, the going theory is that we humans adapted abilities similar to (but not the same as) pokémon in order to survive among them and better connect with them. Of course, because we’re not pokémon and because we don’t actually need our abilities to survive as a whole (just to better handle our pokémon partners), this is, in short, why our abilities are so erratic and wild compared to pokémon.
Rambling aside, the short answer is we just don’t know, but we do know that our abilities are only superficially like a pokémon’s.