A true psychic or medium will rarely label themselves, most people who do are people who are just like everyone else (aka, a little psychic) and just want to feel special
'Psychic' is a general term for anybody with an open third eye. In other words, anybody who can has clairvoyance, precognition, telepathy of any kind. Even empathy can come under that. Every one can be 'psychic'.
i've got psychic abilities, but i hate psychics, or people who say they have psycic powers and the like. don't know why, they've just always rubbed me the wrong way [anyone seen long island medium? yea, i think of people like that] everyone to some degree is psychic, it comes down to practice. myself i was born able to see/hear spirits, and predict things, so it's just normal. now i'm older i have to work at them, but it's just because i enjoy it, not to show off. it's who i am.
anyway, dreams can be interpreted, there's a difference between predictions though ones dreams and foreseeing the future though ones dreams [what's most comon for my family] . i recomend you look into dream interpretation, while not all dreams have deep meaning, most have symbols our mind wants us to take note of. as we sleep our brain keeps working, and many times it'll work out subtle things it noticed but your eyes didn't throughout the day, and it wishes to warn you in your dream. when it comes true, people tend to determine they're psychic, when it's merely observation.
predicting events in your dream however is far more precise. something [example a bird] could tell you in your dream 'you sister's going to break her arm tomorrow' and tomorrow it'll happen. or you could see yourself walking down a street and find a puppy. a week later, you walk down the exact same street, wearing the same clothes in the dream, and find in the same spot the identicle puppy.
myself, if i have a reoccuring dream the thing that keeps happening will come true, but it'll take a while or if i dream someone dies, one week later they will. [though typically i see pet's deaths]