The resolution or adjustability is a result of the pot geometry, dimensions element materials and construction and wiper design, the number of turns is not directly related - for example a trimpot with 20+ turns may have no better resolution or adjustability than a single-turn trimpot with similar electrical element length.
Wirewound pots have a resolution because of the windings of resistance wire. Cermet, conductive plastic, carbon, and hybrid types (such as conductive plastic over wirewound) have “infinite resolution” so substitute the “adjustability” spec from the datasheet. For example, the 3296 series of 25 turn trimpots claims 0.01% adjustability as a voltage divider, a fairly optimistic number.
In the case of wire wound pots, the resolution is also dependent on the element resistance value. Take a typical 10-turn panel potentiometer, the inexpensive plastic-housed 3590 series from Bourns:
The resolution (as a voltage divider) is given as a percentage. So a 10K pot will have a resolution of 0.02%, regardless of the voltage across it (within reason, at very low or high voltages other effects will manifest).
Similarly, with gain, the percentage will be the same, but it will represent more or less voltage depending on the value of gain employed.
The resolution of the 10-turn pot of this design is particularly good because the element is physically very long- it’s helical in geometry. Trimpots may have a mechanical reduction gearing and a short element length, so easy to set but not much, if any, improvement in resolution/adjustability over a single turn pot with the same element length.
If you want to improve resolution with a given pot, you can reduce the range of adjustment with external resistors (temperature effects must be considered more carefully). If you restrict the adjustment range to, say, 9.5V to 10.5V then you have resolution of +/-0.02% of 1V rather than 10V, so you should be able to set it to within +/-200uV in 10V. How long it stays there is another question..
Just as my personal rule of thumb, if better than ~0.1% stability of a precision pot setting or ~1% stability on a non-precision pot is required (these are not hard and fixed numbers but also relate to expected re-calibration intervals (if any), how extreme the conditions are etc.), it's better to re-think the design and add ranges or otherwise reduce the sensitivity to the pot setting. Nowadays we can often replace calibration and setting pots with digital methods.