Difference in Ring/Silent switch and "Do Not Disturb" setting
There are some very significant differences in methods of putting your iPhone 6S plus into silent mode. The mechanical Ring/Silent Switch turns off the phone ringer and keypad dialing tones and I believe other tone notifications. However, do not be fooled as I was. The "Do Not Disturb" setting selected either through Settings/Do Not Disturb or by swiping up from the bottom of the home screen do not render the phone silent. In "Do Not Disturb" keypad tones are still present when dialing and most notably certain inbound calls will ring through. You can select for favorites, specific groups or repeat calls to ring through--and the default is to allow some through. So do not be fooled. Do Not Disturb should default into a totally silent mode and require positive action to allow sounds through.
iPhone 6 Plus, iOS 9.3.1