RelayState is a term from SAMLTwodotZero that refers to a parameter supported by SAML bindings that pass SAML messages through a web browser. A request can include this information and the responder then returns the information with its response, allowing the requester to reconnect the response to any locally-relevant state.
SAMLOnedotOne doesn't formally have the concept of RelayState, but has a one-way mechanism, the TARGET parameter, used in both BrowserProfiles. It's usually been interpreted/used as being the URL of a resource at the ServiceProvider to access once a session is built.
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Going forward, I would expect this to be the model used, and that we would generally not use the RelayState mechanism defined in that specification.