Please verify the use of photos from photo stream please

Hi, this is probably a dumb question but I'm getting confused here. K, so photo stream. Got it on my iphone and in iPhoto. I take a picture with my iphone. Boom it's in photo stream and camera roll. I open iPhoto, go to photo stream or events, after some time, boom my photo is there. But now if I connect my iphone and open iPhoto and import my photos, it will say photo already exists right. So here's where I get a touch confused. Is that photo now actually on my HD or still in the cloud? If I delete that photo from a say from photo stream on my iphone. Does it disappear on my iPhoto or is it on my HD now. Basically what I'm noticing is there are pictures in my iPhoto library that weren't imported off my phone but are on there cause of photo stream. My library is just a mess with stuff missing, stuff that was imported via plugging in and some thru photo stream. If someone could please verify the proper use of this feature I would really appreciate it, thank you