Crypto-assets and central bank digital currencies (CBDCs) are reshaping how value is exchanged in distributed computing environments. These systems combine cryptographic primitives, protocol design, and system architectures to provide transparency and efficiency while raising critical challenges around privacy and regulatory compliance. This survey offers a comprehensive overview of privacy-preserving digital payment systems, covering both decentralized ledger systems and CBDCs. We present a taxonomy of privacy goals -- including anonymity, confidentiality, unlinkability, and auditability -- and map them to the cryptographic primitives, protocols, and system architectures that implement them. Our work adopts a design-oriented perspective, linking high-level privacy objectives to concrete implementations. We also trace the evolution of privacy-preserving digital payment systems through three generations, highlighting shifts from basic anonymity guarantees toward more nuanced privacy-accountability trade-offs. Finally, we identify open challenges, motivating further research into architectures and solutions that balance strong privacy with real-world auditability needs.

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