Both Sony A6500 and Sony A7 III have 24.0 MP resolution sensors but Sony A6500's sensor is APS-C (23.5 x 15.6 mm ) and Sony A7 III's sensor is Full frame (35.8 x 23.8 mm ).
Since Sony A7 III's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Sony A6500.
Below you can see the A6500 and A7 III sensor size comparison.
As seen above, Sony A7 III has a 2.3x Larger sensor area than Sony A6500. 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.