Today, a teammate of mine DMed me on Twitter. I received it as a text message on my iPhone, and did not realize it was a DM through Twitter. When I replied to what I thought was a simple SMS message, Twitter posted it into my public tweet stream.
My colleague saw the public tweet, told me about it, and then I deleted it from Twitter.
Be very careful when replying to text messages. You may inadvertently publicize information that you think you are keeping private.