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Backscatter Communication (BackCom) nodes harvest energy from and modulate information over external carriers. Reconfigurable Intelligent Surface (RIS) adapts phase shift response to alter channel strength in specific directions. In this paper, we unify those two seemingly different technologies (and their derivatives) into one architecture called RIScatter. RIScatter is a batteryless cognitive radio that recycles ambient signal in an adaptive and customizable manner, where dispersed or co-located scatter nodes partially modulate their information and partially engineer the wireless channel. The key is to render the probability distribution of reflection states as a joint function of the information source, Channel State Information (CSI), and relative priority of coexisting links. This enables RIScatter to softly bridge BackCom and RIS; reduce to either in special cases; or evolve in a mixed form for heterogeneous traffic control and universal hardware design. We also propose a low-complexity Successive Interference Cancellation (SIC)-free receiver that exploits the properties of RIScatter. For a single-user multi-node network, we characterize the achievable primary-(total-)backscatter rate region by optimizing the input distribution at scatter nodes, the active beamforming at the Access Point (AP), and the energy decision regions at the user. Simulations demonstrate RIScatter nodes can shift between backscatter modulation and passive beamforming.