For quick context, modern monitors still use signaling that isn't much different than how CRTs operated. There's three main parts to them:
- The actual pixel data
- H-Blank period, which is when the CRT shuts off the electron gun to steer it to the left side the screen (start of a new line)
- V-Blank period, which is when the CRT shuts off the electron gun to steer it to the top of the screen (start of a new frame)
V-Sync forces the video card to hold off on presenting the frame it just rendered until the next V-Blank period. This can cause the stuttering you experience, depending on whenever the video card gets back to rendering the next frame in the 60Hz window.
With an uncapped frame rate, you're seeing the latest information. And the reason you don't see any tearing may simply be from there being not a significant enough of a difference between frames to actually notice, and it also depends on when the frame was rendered.
Another issue with stuttering is frame pacing. Average frame rate doesn't really tell anything other than how many frames were rendered in a second. You could have points in that second where clumps of frames were rendered in a really short period of time with longer periods of time between frames. Frame pacing of 16ms across a second is 60 FPS, but so is half the frames rendered in 8ms, then the other half rendered in 33ms.