Taking photos/videos go to the Camera Roll, then the photo stream. That is how it works. If you do not want the photos to go into the Stream, turn off PhotoStream in the settings for either the iCloud or the Photos. Photostream is like a 30 day backup that takes up valuable space in the iCloud.
Personally, I do not use the photo stream and keep it turned off 99% of the time. The only time I use it is when I want to show a larger version of the photo on my iPad as opposed to the iPhone.