Hi,
According to your post, my understanding is that you want to know the difference of the SharePoint three type user authentications.
Windows claims-based authentication uses your existing Windows authentication provider (Active Directory Domain Services [AD DS]) to validate the credentials of connecting clients. Use this authentication to allow AD DS-based accounts access to SharePoint
resources. Authentication methods include NTLM, Kerberos, and Basic.
Forms-based authentication can be used against credentials that are stored in an authentication provider that is available through the ASP.NET interface
SAML token-based authentication in SharePoint 2013 requires coordination with administrators of a claims-based environment, whether it is your own internal environment or a partner environment.
There is a good article contains all the SharePoint Authentications, including how they work and how to configure.
http://sp77.blogspot.com/2014/02/authentication-in-sharepoint-2013_5.html#.VFcyQ_mUfkJ
Thanks & Regards,
Jason
Jason Guo
TechNet Community Support
