These three types of mental illness are different in both symptoms and known causes. Schizophrenia has genetic precursors, and is neither trauma or chemically induced. The schizophrenic has difficulty perceiving the difference between reality and illusion. The other two disorders do not involve hallucinations, although reality may be distorted in those conditions as well.
Bipolar disorder (often called Manic Depression) is chemical in nature, in that a person develops a chemical imbalance in the body and brain that leaves the person prone to emotional and physical "highs" or "manic" phases where they feel invincible, euphoric and overly energetic, followed, at various intervals, by severe depression marked often by sleeping 20 hours per day, suicidal ideation and difficulty functioning in professional or personal relationships. It is treatable with medication as is Schizophrenia, but there is no known cure.
Dissociative Identity Disorder, formerly known as Multiple Personality Disorder, is neither chemically nor genetically acquired. It is commonly believed that it results from extreme and sustained traumatic events, especially in early childhood, where the person's mind creates distinct identities, exclusive from one another, that interact with the environment completely differently. It is also coupled with amnesia about what happened during a dominant phase of one of the other personalities. This disorder is treatable with therapy, and at generally high success rates.