Hi LowTec,
You can think of the STS as being claims providers with claims coming in and claims going out.
In the case of the STS being an Identity Provider (here is where the orginating authentication for the user happens), the claims coming in is typically some sort of credential (u/pwd, x509 cert etc...) and the STS issues a set of claims to the requestor.
In the case of the STS being a Federation Provider (intermediate claims provider between the Identity Provider and the Application/Relying party), the claims come in as a SAML token and they get validated based on the token signature of the Issuer of this token. The STS may also do further validation on claim values (for e.g does the email address have "@contoso.com" as a prefix since the Issuer is CONTOSO) prior to transforming the claims to the next node (in most simple cases the Application/Relying Party).
The application/Relying Party typically does not send claims typically. When a user attempts to access the application, the application simply, by virtue of policy, asks the user to authenticate from a STS it trusts and when the issuer comes back with a token validates this token and extracts the claims for it.
Hope this clarifies and helps. I'm not sure which white paper that you've read, but David Chappell's white paper available at
http://download.microsoft.com/download/7/d/0/7d0b5166-6a8a-418a-addd-95ee9b046994/Introducing_Geneva_Beta1_Whitepaper.pdfisusually a goodhigh level one.
Thx
--Sam