Different identity systems make different assumptions about the necessity, appropriateness and trustworthiness of a 3rd party identity provider being involved in identity transactions.
There is a 'paranoia continuum', from simple browser SSO (as supported by SAML & OpenID) where the IDP is involved real-time and 'sees' much (to the horror of the anti-panopticonists) to the other extreme where no 3rd party is involved at all (with its own issues).
In between are models where 3rd parties are involved, but trusted less and so constrained more (through client capabilities not available to dumb browsers).
Here are some identity systems plotted onto the paranoia continuum as I see them.
The shading is meant to roughly represent level of support, e.g. SAML's ECP enables the "OK, but I'm watching you" model as supported by Infocards but it hasn't been widely deployed.