Both Casio EX-Z450 and Ricoh GXR GR Lens A12 28mm F2.5 have 12.0 MP resolution sensors but Casio EX-Z450's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Ricoh GXR GR Lens A12 28mm F2.5's sensor is APS-C (23.6 x 15.7 mm ).
Since Ricoh GXR GR Lens A12 28mm F2.5'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 Casio EX-Z450.
Below you can see the EX-Z450 and GXR GR Lens A12 28mm F2.5 sensor size comparison.
As seen above, Ricoh GXR GR Lens A12 28mm F2.5 has a 13.2x Larger sensor area than Casio EX-Z450. 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.