That screw on the carb is for setting the base idle speed but with governor idle there a running idle speed control by governor spring. With governor idle as the engine warms up it needs to close the throttle a little more to control the idle speed; hence, the base idle speed adjustment and a governed idle speed adjustments.
I am surprised the difference between the two is so close when compared the Briggs setup that has nearly 500 rpm difference.
Now the X350 can have a FS600V or FS651V but the adjustments are the same. Just in different positions.
If you have the FS600V use the following link for service manual. The adjustment procedure is in the maintenance section.
https://mymowerparts.com/pdf/Kawasa...anuals/FS600V-FS541V-FS481V-99924-2094-01.pdf