Can anyone explain what the FedAuth cookie is and how it differs from the ASP.Net ASPXAUTH cookie?
FedAuth Cookie is what is used with Claims Authentication. SharePoint STS will issue the FedAuth Cookie which contains the references to the claims token. Claim tokens are actually stored separately.
I believe the ASPXAuth cookie stores the actual user (as SharePoint recognizes them) and whether they are currently authenticated.
They work together, and with claims authentication in SharePoint you have to have both (if you delete your FedAuth Cookie, SharePoint won't like it).