In my research at the Windbridge Institute, we use the term medium to describe an individual who experiences regular communication with the deceased. This is in contrast to a psychic who regularly experiences information about or from people, events, places, or times unknown to him/her.
It is often said that all mediums are psychic but not all psychics are mediums.
Anyone can have mediumistic and/or psychic experiences and the terms medium and psychic are used specifically to describe people who have those experiences regularly, reliably, and often 'on-demand'.
At the Windbridge Institute, we have been performing research since 2008 with a team of mediums whose abilities have been demonstrated under controlled conditions. This allows us to study the phenomenon with participants who are able to effectively and repeatedly provide information about the deceased during various research protocols.
For more info, see:
Beischel, J. (2015). Investigating Mediums: A Windbridge Institute Collection. Tucson, AZ: Windbridge Institute (Blurb).