Single Frame mode on the Nikon D7200 produces one picture each time you press the shutter button. In other words, this is normal-photography mode. Quiet Shutter Release mode works just like Single Frame mode but makes less noise as it goes about its business.
Designed for situations when you want the camera to be as silent as possible, this mode disables the beep that the autofocus system may sound when it achieves focus. (The beep sounds only if you enable it through the Beep setting on the Custom Setting menu; it's turned off by default.)
Additionally, Quiet Shutter Release mode affects the operation of the internal mirror that causes the scene coming through the lens to be visible in the viewfinder. Normally, the mirror flips up when you press the shutter button and then flips back down after the shutter opens and closes. This mirror movement makes some noise.
In Quiet Shutter Release mode, you can prevent the mirror from flipping down by keeping the shutter button pressed after the shot. This feature enables you to delay the final mirror movement — and its accompanying sound — to a moment when the noise won't be objectionable.
