Sony A7R III has a 42.0MP Full frame (35.9 x 24 mm ) sized BSI-CMOS sensor and features Bionz X processor. On the other hand, Samsung NX mini has a 20.5MP 1' (13.2 x 8.8 mm ) sized BSI-CMOS sensor .
Sony A7R III's sensor provides 21.5MP more than Samsung NX mini's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Another difference between these two cameras is that Sony A7R III's sensor lacks anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the A7R III and NX mini sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A7R III and Samsung NX mini Cameras
As seen above, Sony A7R III has a 7.4x Larger sensor area than Samsung NX mini. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.