A selectable one-way clutch (SOWC) assembly uses hydraulic-actuation to select operating modes within a rotating housing. Two races of the SOWC assembly can rotate at disparate speeds, i.e., one race is not grounded prior to actuation. The SOWC assembly has a pair of races keyed to different housings and hubs. The housing and hub can be attached to different elements of a gear train, for example, which can be rotating during the various gear states. A hydraulic actuator or multiple actuators can be keyed to the housing, with axial motion of the actuator or actuators selecting a state or operating mode of the SOWC assembly. The actuator has axially-extending tabs that engage radially-extending fingers of the selector plate, thus rotating the selector plate in different directions when applied or released. Multiple actuators can be used in conjunction with multiple selector plates to provide additional SOWC operating modes.