Cryptosystem

There are two different meanings of the word cryptosystem. 
General meaning.
In this meaning, the term cryptosystem is used as shorthand, or as an abbreviation for "cryptographic system". A cryptographic system is any computer system that involves cryptography. Such systems include for instance, a system for secure electronic mail which might include methods for digital signatures, cryptographic hash functions, key management techniques, and so on. 
Meaning in the cryptographic community.
In this meaning, a cryptosystem refers to a set of algorithms needed to implement a method of encryption and decryption. 
Typically, a cryptosystem consists of three algorithms: 
The term "cipher" (sometimes "cypher") is often used to refer to a pair of (encryption/decryption) algorithms. Therefore, the term "cryptosystem" is most often used when the key generation algorithm is important. For this reason, the term "cryptosystem" is commonly used to refer to public key techniques; however both "cipher" and "cryptosystem" are used for symmetric key techniques.
"Cryptographic system" vs. "cryptosystem".
The "Internet Security Glossary" advises against using the term "cryptosystem", giving the following definitions.