What the claim of type http://schemas.xmlsoap.org/ws/2005/05/identity/claims/nameidentifier should be used for?
This is the main question, and here are
The nameidentifier claim should be used for getting a unique user name.
For Windows Authentication:
http://schemas.xmlsoap.org/ws/2005/05/identity/claims/nameidentifier domain\warlock
http://schemas.xmlsoap.org/ws/2005/05/identity/claims/name 0#.w|domain\warlock
domain\warlock is a Windows Login name
For Claims Based Authentiacation:
http://schemas.xmlsoap.org/ws/2005/05/identity/claims/nameidentifier warlock@localhost.com
http://schemas.xmlsoap.org/ws/2005/05/identity/claims/name 05.t|myidentityprovider|warlock@localhost.com
email was specified as the Identifier Claim
As you can see .../identity/claims/name describes name and identity provider as well.