Being psychic means that you are connected to your past lives and generally connected with spirits. Like the Psychic Twins, they have unlocked their claircognizance ability along with the other 3 clairs. I am, right now, only claircognizance. With the help and practice of automatic writing, i could connect to spirits to help me gain a future prediction, or a past life prediction, or to give simple advice. It is also used to detect liars. Though you cannot abuse this power to like cheat on lotteries and stuff. It is a gift, do not abuse it. Do you know that moment when someone asks you a question like, How much salt have I added into this solution. And you guessed the right amount. Yea, that's called being psychic. There is a difference between this and reading minds. Remember that reading minds is impossible. This is you connecting to you spirits for a few second and getting the right answer. Skeptics call it being lucky, superstitious people call it being psychic.
A mentalist picks up on physical cues to read a person by their actions. Some may also perform hypnosis, and most are thoroughly versed in NLP. Basically, they know how the mind works to a degree that they can read and manipulate people.
A psychic will read via some sort of metaphysical means. That is, they will have a sense or feel a 'vibration' related to something. Some may use divination, and practice both psychic work and divination at the same time with not only intuitive readings, but also while 'feeling' the energy of the querent. There are some who can meet a person and know part of their story without asking.