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 in order to integrate their cryptographic hardware.
A CNG (Cryptography API Next Generation) is the second-generation cryptographic interface developed by Microsoft. It offers updated cryptographic algorithms and is intended for a long-term replacement of CSP.