A psychic is someone that uses extrasensory abilities to reveal hidden information, information unattainable through our physical senses such as sight and hearing. The individual may possess abilities such as clairvoyance or clairsentience though there are as many psychic abilities as there are physical senses. These individuals read the energies and interpret the meanings using their psychic ability.
Someone who is identified as a medium is able to sense and communicate with the dead. Not all mediums see the spirit of a dead person, some mediums may only be able to hear them or feel them, but all are able to communicate with the dead. Some mediums will use tools like Spirit Boards, mirrors, tables, or cards to aid in the communication process. There are many different types of mediumship abilities that an individual is able to possess, but the defining ability is communication with those individuals who have died.
A Witch is someone who has established a relationship with both the physical realm of existence and the spiritual realms of existence; both the forces of nature and the forces of Spirit. He or she practices the Craft, which is how the Witch is able to manipulate the energies of these realms in order to facilitate a change in reality. Witches use their innate psychic abilities when they practice conjuration, divination, dowsing, prophecy, remote viewing, astral projection, and scrying; though not all Witches will do all these things many of them will. The Witch is aware of their own energy as well as the energies surrounding them whether it is from the natural environment or another sentient being.
All Witches are psychic, but not all psychics are Witch.
All Witches are mediums, but not all mediums are Witch.
All Witches are empaths, but not all empaths are Witch.
I do believe that someone could be a combination of empathy, psychic, and medium or identify as just one of them, but I do believe that a Witch is inherently all of them combined though he or she may not have yet discovered one or more of their abilities.