Psychiatrist: These are medical doctors, trained to diagnose issues in body chemistry as well as, or contributing to mental disease. As a method of treatment, they usually prescribe medication, and in some less common cases, choose to use psychology. In essence they strive to mask, control or heal a "condition" (i.e. schizophrenia). In extreme cases like this, psychiatry can be very beneficial, so that you may function in daily life.
Psychotherapist: Is a healer of the "psyche"; the "mind". They discuss emotions and thoughts related to the problem, violation, cause, of the issue or trauma to reach a mental and logical understanding of it and what transpired thereafter. They diagnose conditions of behavior. In essence, they help you mentally understand what happened, and why you reacted to it as you did. There are only a small number of states, that allow them to dispense medication.
Psychic: A psychic will give a "reading" to determine why the soul felt the need to experience the trauma, what was the purpose of it, and give tools to help heal and resolve it on a physical, mental, emotional and energetic/spiritual/soul level, through or suggesting: shamanic healing, spirit removal, depossession, past-life therapy, mediumship, crystals, meditation, auric cleansing, herbs, higher level of forgiveness etc. depending. These individuals may or may not have had formal training. The quality of the recommendations depends on the level of accuracy of the psychic. Some may be skilled in the other modalities recommended, and can thereby also offer treatment. In essence, they provide the reasons why something is happening to you, that may not be readily apparent, or outside the realm of college training, and in some cases they themselves can provide treatment for you, depending on their skill level. Their goal is to go beyond understanding and treating an issue mentally or physically, and instead release you from it. Psychics can include the fields of healers, mediums and to some degree even astrologers.