Any time you have a mismatch between frame rate and refresh rate, there will be judder. This means that the length of time that the frame appears on the monitor does not match the length of time that was simulated in the game world for that frame. If the frame rate is constant then the judder pattern will be regular. If you are in exclusive fullscreen then you will also get tearing.
Imagine the blue are the 75Hz display refresh periods. 13.3ms each. The orange are the rendered frames at 100fps, 10ms each. For the first refresh of the monitor, it will be mostly one frame, with a tear line and the bottom 25% will be of the next frame. The second refresh will be half each of two frames, and then the third again will be like the first. Of course in real life it will not be as tidy as this but you get the idea.
The motion will not look smooth because the amount of time being simulated will not match the amount of time the images are on the screen, and different images will appear to be on the screen for different lengths of time. It is the same effect as when you play a 24fps video on 60Hz screen, or 60fps video on 75Hz screen. Camera pans will not be smooth and appear jittery, this is judder.
If you want smooth motion you need to either match the frame intervals to the refresh intervals with vsync, or use freesync/gsync which does the opposite and adjusts the display interval to match the framerate.
Having said all that, if you are getting 500fps this should not be noticeable. 500fps is so fast that there would be multiple updates per frame and it would look smooth, even the tearing would be hard to spot. It will be a factor at lower framerates though.
There is another thing that could cause it, it could be your mouse. To test for this, go into a first person game and strafe left and right using the keyboard only. Now do the same thing but also move the mouse smoothly from left to right. If your mouse has a low polling rate you might see that the keyboard-only movement is much smoother than the mouse movement. It's all very well to render 500fps but if the mouse is only updating at 100Hz then only every 5th frame will have an actual update to draw. So while other objects in the world will look smooth at 500fps, the camera movement would effectively be only 100fps, and you would get judder as well. If this is noticeable for you then it might be worth trying a mouse with a 500Hz polling rate.
The mouse thing will of course be different in different games, some games will smooth the mouse movement over multiple frames, some will do predictive rendering and draw "fake" interpolated frames in between the actual simulated ones, and stuff like that.