Deja vu is when you see something, and you get a really strong feeling that you have been there before and experienced exactly the same thing.
A premonition is like in the movie The Fional Destination, where the guy is on a plane and he's waiting for it to take off, and he falls asleep and he has a totally vivid dream that the plane has taken off and catches fire and crashes and everyone dies. And then he wakes up and thinks "omg we have to get off the plane now." So he shouts at his friends to get off the plane and they listen to him/get thrown off and the plane takes off, and then it crashes and everyone still on the plane dies. Except for the guy who had the premonition and his friends. (Only that's not the end of the story...)
Premonition is when you have a feeling that something is about to happen. Deja Vu is when you feel like a situation has happened before and is now happening again.
A premonition is something you "see, feel or hear" happen before it happens. A "deja vu" moment is when you see, hear, feel or experience something that makes you feel like you've done it, seen it, heard it, felt it or experienced it before. Example-You get the feeling someone is going to call you from out of no where, then that person calls (premonition). Your walking down the street and you see a pair of shoes in the window of a shop. You suddenly feel like you've done this and seen this before but know you haven't. I get both experiences quite a few times a month.
Deja Vu begins in your sleep and you cannot remember it when you wake up. Sometime later, you have a feeling that you've seen this or remember this or hear this from somewhere. Premonitions is when you do remember it and you usually see it before it happens. It necessarily doesn't happen during sleeping. If it does, then you will most likely remember it.
Premonitions are when you have a distinct and unusual feeling that a certain event will occur in the future (maybe the near future).
Deja Vu (from the french, meaning, "Seen already") is when you realize that something that you are doing/saying or something that's happening has already occurred to you in the past.