Why equate "Credential Service Provider" to "Identity Service Provider"?

[whitehatguy]

This publication seems to indicate that "Credential Service Provider" is analogous with "Identity Service Provider", but the definition provided for CSP doesn't align 1:1 with the ITU definition for IdSP [1]. The former assigns credentials, the latter may or may not assign credentials to individuals associated with such identities. A CSP seems to be an IdSP that only assigns identities to individuals whom have also been credentialed.