Psychics get messages in various ways, not all psychics are alike. They communicate their messages to the client. These messages are about their clients lives, loved one's lives, or situations that need to be discussed. Past, present and future messages are possible, but tend to be difficult to specify in all readings. If there are very specific details provided then these psychics may be "evidential" meaning that their gift/training has been taken to the next level, and they can decipher the messages into very specific images, with great detail. This provides clarity, and strong proof of the psychic connection.
Mediums actually communicate with souls that have passed on. In some cases though, these souls might not be dead, but then we change the modus operandi to "telepathy". Mediums can, in some cases allow the spirit to enter their body and in a "sense" share the senses with the visiting spirit or soul. How ever this can be dangerous. Mediums do have psychic abilities as well. As for why not all psychics are mediums is not fully understood, but there are theories regarding this.