The main difference between the two approaches is simple. Parapsychology studies the paranormal with the assumption that reported paranormal events and abilities, such as telepathy and clairvoyance, are real, that people can actually bend spoons with their minds or contact dead people with some form of mediumistic abilities. The focus of parapsychology is on studying paranormal phenomena as though they really happened rather than being the subject of science fiction. The main problem with parapsychology is that there is no scientific evidence for any of the phenomena described.
Anomalistic psychology is the better of the two because it is grounded in real science. It is the scientifically grounded study of people who believe in the paranormal, attempting to explain why they believe in it and the psychological basis for their beliefs. It assumes that paranormal phenomena do not actually exist, but that there are deep-seated reasons why belief in them is common across many societies.