A CSP (Cryptographic Service Provider) is a general-purpose cryptography standard developed by Microsoft. On one side, it defines a cryptographic interface to be used by applications (CryptoAPI). On the other side, it defines an interface to be used by manufacturers to integrate their cryptographic hardware.
A CNG (Cryptography API Next Generation) is a second-generation cryptographic interface developed by Microsoft. It offers updated cryptographic algorithms and is intended as a long-term replacement for CSP.