In this paper, we introduce a variant of reconfigurable intelligent surfaces (RISs) called omni-digital-RISs (DRISs), which allow multiple physical processes, with application to optical wireless communications systems. The proposed omni-DRIS contains both reflectors and refractive elements, as well as elements that perform both simultaneously. We describe and explain the concept of omni-DRIS, suggest and analyze an omni-DRIS coding structure, discuss metamaterials to be used, and provide a design example. Furthermore, we demonstrate that the achievable rate of an omni-DRIS system depends on the number of omni-DRIS elements, bits per phase shift, and the number of unused elements. In addition, we show that the achievable rate upper bound is related to the number of omni-DRIS elements, and conclude by discussing future research directions.