One of the more interesting pieces of evidence that schizophrenia and bipolar are related is in genetic histories. You could have a grandfather with schizophrenia, and a brother with bipolar who has a daughter with schizoaffective disorder, etc. etc. They appear to be variations of a genetic theme.
There is often a great difference in the experience of bipolar disorder and schizophrenia though. People with schizophrenia would generally give their left arm not to have schizophrenia. People with bipolar tend to feel very differently. I recently gave a presentation with a young man with bipolar to a multifamily education session. I asked him about the film "Mr. Jones", in which Richard Gere plays a man with bipolar disorder. It gives him a lot of trouble, but when he has been brought to a hospital by the police and strapped down to a bed, and the doctor tries to explain to him that he has an illness, he yells out in reply "This is not an disease, this is who I am!"
The young man I made my presentation with felt the same way. He identified with his illness much more then I did. My illness makes me do things, my illness interferes with my attempts to do things, my illness is the pits. It has literally wasted my life before my very eyes. Sometimes I wish I had never been born. The young man felt that he was who he was because he had bipolar disorder. He was very proud of who he was. People can be very productive in a state of mild mania. The disease itself is associated with high intelligence and creativity.