Terminology for cryptography varies widely, from informal and colloquial to mathematically-defined, with different precision and formalism depending on whether the stakeholder is a developer, cryptologist, etc. Yet there is a need for CWE to be self-consistent while remaining understandable and acceptable to multiple audiences.
As of CWE 4.6, CWE terminology around "primitives" and "algorithms" is emerging as shown by the following example, subject to future consultation and agreement within the CWE and cryptography communities. Suppose one wishes to send encrypted data using a CLI tool such as OpenSSL. One might choose to use AES with a 256-bit key and require tamper protection (GCM mode, for instance). For compatibility's sake, one might also choose the ciphertext to be formatted to the PKCS#5 standard. In this case, the "cryptographic system" would be AES-256-GCM with PKCS#5 formatting. The "cryptographic function" would be AES-256 in the GCM mode of operation, and the "algorithm" would be AES. Colloquially, one would say that AES (and sometimes AES-256) is the "cryptographic primitive," because it is the algorithm that realizes the concept of symmetric encryption (without modes of operation or other protocol related modifications). In practice, developers and architects typically refer to base cryptographic algorithms (AES, SHA, etc.) as cryptographic primitives.
Maintenance
Since CWE 4.4, various cryptography-related entries, including CWE-327 and CWE-1240, have been slated for extensive research, analysis, and community consultation to define consistent terminology, improve relationships, and reduce overlap or duplication. As of CWE 4.6, this work is still ongoing.