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.
In my line of work, I communicate with Spirit Guides every day, but do I still wonder if they are real? Absolutely. Following is a personal story, on the subject, that surprised and amazed me.
My father went to the doctor for a check up. He had a chest x-ray, and got a clean bill of health. A year later he went back, because he was having shoulder pain, that had become increasingly severe and debilitating. Unexpectedly, he was diagnosed with cancer on the lining of his lung, which had eaten away at his ribs, leaving only points of bone. The diagnosis was terminal, with treatment to shrink the size of the tumor, and medication to keep him comfortable. He came home from the appointment, and sat down with my sister, showing her the new x-rays, and what the doctor had said. He told her that his "Spirit Guide, Tony", had spoken to him and told him that he would come and get him, when it was his time to go. This confused my sister, as my father is a strict Catholic, and has never discussed anything of the sort, much less used a term such as "spirit guide". (At that time, my Dad was not on any medication, and did not have any mental disorders. He had been completely healthy, was full of energy and active.)
Soon after, my Dad needed a morphine pump to help him deal with the incredible pain. He lived through nine months of hallucinations, with short spurts of mental clarity, in a bedridden hell. Shortly before his death, he called me on the phone to say, "I don't think I'm going to make it. I think the cancer's getting me." It was a call for me to come home, because he knew he was dying. I didn't make it there to see him before he passed, and I think that will always haunt me with deep regret. A few days later, he became very lucid, and told my sister that "Tony" was here to get him. And then he was gone later that day.