Both Olympus TG-820 iHS and Casio EX-10 have 12.0 MP resolution sensors but Olympus TG-820 iHS's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Casio EX-10's sensor is 1/1.7-inch (7.44 x 5.58 mm ).
Since Casio EX-10'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 Olympus TG-820 iHS.
Below you can see the TG-820 iHS and EX-10 sensor size comparison.
As seen above, Casio EX-10 has a 1.5x Larger sensor area than Olympus TG-820 iHS. 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.