Paranormal Activity: relating to the claimed occurrence of an event or perceptionwithout scientific explanation, as psychokinesis, extrasensoryperception, or other purportedly supernatural phenomena.
Demonic:
inspired as if by a demon, indwelling spirit, or genius.
The difference between demonic obsession and demonic possession:
Demonic Possession is when a Demon or negative entity takes control of your physical body, making you act in accordance to it's will. Usually this involves negative actions, or self harm.
Demonic Obsession is when a Demon or negative entity becomes infatuated with your presence. They are drawn and attracted to your energy, and physical body. Normally this is a result of a demon that is in need of attention, or a demon lusting after you. In Demonic Obsession they may use tactics to gain your attention by filling your mind with thoughts of them, or inflicting pain to make you think of them.
The Key difference is Control.
In Demonic Possession they can Control your body from the inside.
In Demonic Obsession they attempt to control your thoughts by distracting you, and focusing your attention on them, the Demon itself.