Perhaps you could explain the difference between those rates. If a monitor is set to 144Hz but a game is stuttering does refresh not matter? If the monitor is set to 60Hz and a older game is playing will it be limited to 60fps even if the game reports 100+ fps?
So you have a few options:
Option 1) VSync. This will limit the game from displaying and rendering over the hz on your monitor, and will remove any tearing. Going under your monitor refresh rate can cause hitches as the game will not update until its finished rendering another
Option 2) Unlimited / VSync off. This will let the game render and attempt to display as fast as possible. You can end up with tearing which can be anywhere from "unnoticeable" to very annoying depending on your tolerance.
Option 3) FreeSync (Adaptive Sync) / GSync. This will remove any tearing while inside its range, which is under your monitor refresh rate. Its best for >60hz monitors as it allows more leeway to stay inside the range without having to use vsync / frame limiter.
Option 4) Frame limiter. This will stop the GPU from rendering more frames once you've hit the limit.
You can combine Option 3 with either 1 or 4 for the best experience if tearing bothers you.
Does that help or answer your question?