Intuitive vs. Psychic
Although many people use the terms psychic and intuitive interchangeably, and although they are very close in fundamental nature, they are not the same thing. While all psychics are intuitive, not all intuitives are psychic. Intuition is an unconscious form of knowledge. It is immediate and often not open to rational/analytical thought processes. Intuition differs from an opinion because opinion is based on experience, while intuition is held to be affected by previous experiences only unconsciously. Intuition also differs from instinct, which does not have the experience element at all. Intuition is trans-intellectual, while instinct is pre-intellectual. A person who has an intuitive opinion cannot immediately fully explain why he or she holds that view. However, a person may later rationalize an intuition by developing a chain of logic to demonstrate more structurally why the intuition in valid. Intuition is one source of common sense. It can also help in induction to gain empirical knowledge. Sources of intuition are feeling, experiences and knowledge. These things typically define the Intuitive.

A Psychic, on the other, is someone who is, in most cases, very sensitive to nonphysical forces lying outside the sphere of physical science or knowledge, and exhibit strong sensitivities to nonphysical or supernatural forces and influences.

Psychic vs. Psychic Medium
As with the above between psychics and intuitives, all mediums -- i.e., psychic mediums, after-death communicators, spirit mediums) -- are psychic but not all psychics are mediums. A Psychic's purpose is to provide validating information about the sitter's -- the person receiving the reading -- energy concerning their life issues and spiritual growth whereas a Psychic Medium's purpose is to help provide proof of an afterlife by perceiving validating information from the Other Side (those who have departed from physical living).

The goal of both the Psychic and the Psychic Medium is to create a healing energy that enlightens and helps the sitter on his or her personal journey and does not foster or create a dependency on the reader (the Psychic / Psychic Medium).

Some Psychics can also communicate with the sitter's spiritual guides. In general, the major difference between a Psychic and a Psychic Medium is the adept ability to communicate with those who have crossed over.

Based on the information provided above -- though you will easily find people and resources that disagree with these interpretations -- one can now infer that all mediums are also psychic and intuitive.