Let's say you're using a 60 Hz monitor and playing a game where the GPU fluctuates between 65 and 100 fps if you leave it uncapped.
Nothing: Your GPU renders frames as fast as it can. Your GPU will send each frame to the monitor as soon as the GPU finishes that frame. You get tearing because the GPU can pass a frame to the monitor while the monitor is already in the middle of displaying a different frame. Result: Variable framerate, tearing
Capped fps, no vsync: Your GPU renders frames at 60 fps. Your GPU will send each frame to the monitor as soon as the GPU finishes that frame. You get tearing because the GPU can pass a frame to the monitor while the monitor is already in the middle of displaying a different frame. Result: Consistent framerate, tearing
Regular vsync: Your GPU renders frames at 60 fps. When the GPU finishes a frame, it will sit and wait (not rendering anything) until the monitor is ready. Once the monitor is ready to display a new frame, the GPU will send that frame to the monitor, and only then does it begin to draw a new one. Since the GPU doesn't send frames until the monitor is ready, there is no tearing. And since the GPU always begins drawing right after a frame is sent to the monitor, the frames are always the same space apart (1/60th of a second). Result: Consistent frame spacing, no tearing
Fast sync: Your GPU runs as fast as it can. When the GPU finishes a frame, it will save that frame and immediately begin rendering another. When the monitor is ready to display a new frame, the GPU sends whatever frame it most recently finished. Sometimes the GPU finishes only one frame before the monitor is ready, sometimes it finishes more than one. This means that the spacing between displayed frames varies. Result: Inconsistent frame spacing, no tearing
Fast sync with fps capped near your monitor's refresh rate: Essentially the same effect as
regular vsync.
You probably want regular vsync. Regular vsync is smooth, and the lag is generally not an issue unless frames are queued up (for games that do this, prevent it by setting "max pre-rendered frames" to 1 in Nvidia control panel). Fast sync can offer even less input lag, but unless your GPU is running at very high FPS (think 200+), you will get noticeable stuttering and skipping, and the input lag difference will be trivial.