Sony A7 III has a 24.0MP Full frame (35.8 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz X processor. On the other hand, Nikon D500 has a 21.0MP APS-C (23.5 x 15.7 mm ) sized CMOS sensor and features Expeed 5 processor.
Another difference between these two cameras is that Nikon D500'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 moire occurring in certain scenes.
Below you can see the A7 III and D500 sensor size comparison.
As seen above, Sony A7 III has a 2.3x Larger sensor area than Nikon D500. 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.