The term "differential spoilers" relates to how spoilers augment the roll commanded by the ailerons during speed brake operation. This arrangement maximizes the augmentation of roll control with a small sacrifice in (commanded) profile drag braking.
"Non-differential" spoiler arrangement will augment aileron roll control to a lesser degree during partial extension and when the speed brakes are fully extended, they offer no help.
The example you have given is for a right turn.
the difference between diff. spoiler and non-diff. spoiler is diff. spoiler retract and supplement roll control when speed brake is fully extended.
This is one of the key differences. See below for the rest.
however, if non-diff. spoiler doesnt contribute to roll control, why there is difference between right spoiler and left spoiler?
Non-differential (standard) spoiler deployment contributes to roll control in all but the fully extended speed brake configuration. Another way to think about it is the non-differential spoiler arrangement never reduces profile drag during roll control augmentation.
why right spoiler needs to extend further when speed brake half extended?
To assist with roll control.