One of the latest Snapchat updates is the ability to save a picture or video to one’s camera roll if the content is shared in a private chat. When someone does this Snapchat will display the following:
User replayed your Snap!
User took a screenshot
User took a screenshot of chat!
It also shows the Replay with the red circle as well. So, if you are going to save a picture or video to your camera roll, do not think that you can do this without the other person knowing.