Security Assertion Markup Language (SAML) is an open standard that allows identity providers (IdP) to pass authorization credentials to service providers (SP).
SAML transactions use Extensible Markup Language (XML) for standardized communications between the identity provider and service providers.
SAML is the link between the authentication of a user's identity and the authorization to use a service.
WS-Security is the key extension that supports many authentication models including: basic username/password credentials, SAML, OAuth and more.
A common way that SOAP API's are authenticated is via SAML Single Sign On (SSO). SAML works by facilitating the exchange of authentication and authorization credentials across applications. However, there is no specification that describes how to add SAML to REST web services.
Reference:
https://www.oasis-open.org/committees/download.php/16768/wss-v1.1-spec-os-SAMLTokenProfile.pdf