"Ghost" vs. "Apparition"
A ghost is the appearance of a dead person's spirit or essence. It can be seen, possibly heard, but not touched.
An Apparition on the other hand, although very similar to a ghost, can be anything or anyone from "the beyond". Any spiritual appearance that can be seen is an apparition.
Can't tell the difference? It's subtle at best. Apparition just sounds better to those who investigate the paranormal world.
"Ghost" vs. "Poltergeist"
The distinction here is much clearer. A poltergeist is usually much more destructive or at the very least, mischievous. Poltergeists are often said to throw stones, slam doors, start fires, rattle pots and pans and irritate household pets.
Ghosts are not known for causing trouble. They are more likely to do something subtle to get your attention - like dim the lights or make a candle flicker.
"Supernatural" vs. "Paranormal"
Something that is supernatural usually has some basis in spiritual or demonic forces. Supernatural occurrences cannot be explained by scientific or natural known laws of nature.
Paranormal also cannot be explained by scientific or natural laws of nature. So the difference? Well, the people delving into the occurrences prefer to use the term paranormal, simply because it does not have the same religious feeling to it.
"Amulet" vs. "Good luck charm"
An Amulet is an object thought to possess supernatural powers. Often an amulet is used to ward off evil spirits or demons. The Egyptians of old often used a type of quartz called "chalcedony" as an amulet, attributing to the stone the power to keep them safe, especially from night time travelers from the "other side".
A Good Luck charm does not necessarily work for every one. It is said to only bring luck to one person. A four leaf clover, a rabbit's foot, lucky underwear, lucky socks - these are all things that are said to being the owner luck - but are not purported to keep supernatural bad guys away.