Paranormal investigators say they look for evidence of paranormal activity. That phrase always confounded me. I don't quite get it. What does it mean when someone says they have evidence of "paranormal activity"? And, how do you know it's not normal activity that you just couldn't ferret out?
There is a problem with how the word paranormal is used because it is often utilized in a way that is perhaps not consistent with the original intent.
Language evolves. Let me take a shot at unpacking some of these definitions about unexplained phenomena. See if it makes sense.
"Paranormal" and other terms for strange goings-on have changed over time. The word paranormal was coined around 1920. It means "beside, above or beyond normal." Therefore, it's anything that isn't "normal" -- or, more precisely, it is used as a label for any phenomenon that appears to defy scientific understanding. Ok, right there is a tripping point. Whose scientific understanding? The observer who is calling it "paranormal"? If so, that is problematic as a theoretical physicist sees things a lot differently than a dentist or a police officer. So, it appears too subjective to be precise. Each person may have their own idea of what constitutes "paranormal activity".
The term "paranormal" used to just mean extrasensory perception and psychic power but, since the 1970s in particular -- thanks to TV shows and proliferation of the subject in popular culture -- the term expanded in scope to include all mysterious phenomena seemingly shunned by standard scientific study. It was a convenient way to bring many similarly peculiar topics under one heading for ease of marketing. So today, it can include everything that sounds mysterious: UFOs, hauntings, monster sightings, strange disappearances, anomalous natural phenomena, coincidences, as well as psychic powers.
Not everyone agrees that fields of study such as UFOlogy or cryptozoology (Bigfoot, Loch Ness Monster and the like) should be considered paranormal but, if we think about the fact that after all this time, we have yet to document what these things actually are, that is beyond normal. Therefore, paranormal (arguably).
What appears as paranormal could essentially one day become normal. This has happened before with meteorites and still mysterious but likely explainable earthquakes lights and ball lightning. Or, we might not have developed the right technology or made the philosophical breakthrough yet to provide an explanation for some seemingly paranormal events. Perhaps we may find an instrument that can measure whatever it is that results in "hauntings" of a particular type. (Notice that I didn't say an instrument that detects ghosts -- an important distinction.)
Contrasted with paranormal is "supernatural." To say something is supernatural is to conclude that the phenomenon operates outside the existing laws of nature. We would call such phenomena miraculous, a result of religious, occult (or magical) forces that are outside of human doings. These forces don't adhere to boundaries of nature, which are waived. Perhaps the entity decides not to be detectable, for example. When that happens, we can't test it, capture it or measure it. We just broke science. Our understanding stops if the explanation allows for supernatural entities to suspend natural laws on a whim. We end up with a form of "[Insert entity name here] did it." Game over.
Paranormal events can appear to be supernatural but that in no way is proof that they are. Some unaccounted for natural explanation can be the cause. There is really no way to have excluded all natural possibilities in an investigation. We just may not have all the information. So to say something is the result of "paranormal" or "supernatural" activity is faulty logic. It can appear to be but you can't say that it is for sure.
If you look at older anomalistic literature, you'll find the word "preternatural" -- a perfectly cromulent word -- in place of paranormal. It's not used as much anymore but it denotes a situation where the phenomenon appears outside the bounds of what we consider normal. It's not supernatural, just extraordinary.
An even better word to use for weird natural phenomena -- like strange falls from the sky (frogs, fish, colored rain), mystery sounds and lights, odd weather phenomena, etc. (things that might also be called Fortean) -- would be paranatural. Events seem beyond natural because they are rare, unusual and we can't quite pinpoint how they happened, but we need not revoke natural laws to have them occur. It's similar to preternatural but sounds more modern.
Sorry about the word salad in this post but terminology is rather important for effective communication in order to avoid being misunderstood. These various words reflect the degree to which you want to go beyond observable, experimentally derived evidence. They get progressively LESS likely to be the correct designation: Paranatural -> paranormal/preternatural -> supernatural (which we can't actually "prove").
Pedantry over. We now resume normal communication.