Panasonic G9 has a 20.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor . On the other hand, Panasonic ZS35 has a 16.0MP 1/2.3-inch (6.08 x 4.56 mm ) sized CMOS sensor .
Another difference between these two cameras is that Panasonic G9'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 G9 and ZS35 sensor size comparison.
As seen above, Panasonic G9 has a 8.1x Larger sensor area than Panasonic ZS35. 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.