The Heavens Angels

What is a Medium? (definition from Wikipedia)
The term "mediumship" denotes the supposed ability of a person (the medium) to experience and/or to tell others about their experiences of contact with spirits of the dead, spirits of non-corporeal entities, angels, and/or nature spirits. By experiencing these visions, the medium generally claims to allow communication between non-mediumistic people and spirits who may have messages to share.

A medium may claim to: listen to and relate conversations with spirit voices; go into a trance and speak without knowledge of what is being said; allow a spirit to enter his or her body and speak through it; or relay messages from the spirits those who wish to contact them with the help of a physical tool, such as a writing pad.

Mediumship is also part of the belief system of some New Age groups. In this context, and under the name channelling, it most often refers to a medium purporting to receive messages from a "teaching-spirit" of advanced wisdom.
In some cultures, mediums (or the spirits working with them) are imagined to be able to produce physical paranormal phenomena such as materialisations of spirits, apports of objects, or levitation

What is a Psychic? (Definition from Wikipedia)
In popular culture the word psychic (from the Greek psychikos - "of the soul, mental") refers to the ability to perceive things hidden from the senses through means of extra-sensory perception. The term also refers to theatrical performers who use techniques such as prestidigitation and cold reading to produce the appearance of having such abilities. Parapsychologists attempt to study what some believe are psychic phenomena using a variety of methods such as random number generators to test for psychokinesis or the Ganzfeld experiment to test for extra-sensory perception.

Early examples of individuals thought by some to have psychic powers include the Oracle of Apollo at Delphi who was thought to provide prophecies from Apollo himself as well as Nostradamus, a French apothecary who is thought by some to have had the ability to predict the future. During the 19th century belief in psychics became more common and many notable individuals gained notoriety including Daniel Dunglas Home. Psychics are also very popular in science fiction today and many works of fiction include individuals with psychic abilities, including The Dead Zone by Stephen King as well as Jean Grey from the Marvel comic book universe. Today, belief in psychic phenomena is widespread amongst the general public. A 2005 Gallup poll concluded that 41% of Americans believe in extra-sensory perception.

The existence of extra sensory psychic abilities is disputed by skeptics who contend that there is no scientific evidence supporting such abilities and apparent psychic phenomena are nothing more than intentional trickery or self delusion. Debunker James Randi has offered a $1 million prize to any individual who can, under controlled circumstances, demonstrate any paranormal or supernatural ability. As of yet, Randi has not agreed terms with any aspirants nor aspirants passed his preliminary requirements.