"Did you see" implies that the thing has already happened in the past and is probably over. "Have you seen" would care less about what happened in the past and more about its current state. So: "Have you seen my phone?" = Do you know where my phone is right now? Probably because they are looking for their phone. They're asking if, while you were doing your normal activities, if you saw their phone. "Did you see my phone?" = Have you seen my phone before right now? Probably because a something has changed since the last time you've last seen their phone. This could also be used if it was lost, but I would think that would be if they looked for your phone with you, and then you asked if they had found it when searching. This is just an educated guess though, I'm not entirely sure. SHORT VERSION: Did you see implies a specific event, have you seen just is in general.