Jeff has updated the SAML Glossary, making it available in HTML.
The SAML definition for 'federation' is:
Federation This term is used in two senses in SAML:
1. The act of establishing a relationship between two entities [Merriam].
2. An association comprising any number of service providers and identity providers.
For some, 'federation' in the latter sense is synonomous with a 'Circle of Trust', this interpreted as some group of providers, the CEOs of which have had drinks together in some swank restaurant, the lawyers of which have had thrashed out detailed legal agreements governing the identity transactions of their shared customers, employees, citizens etc, and the IT staff of which have exchanged metadata, crypto keys, and complaints about their respective CEOs. This is Big Business.
But of course the above definition says nothing about the rules by which membership in the "club" is defined.
Often times the rules will (as in the Big Business case) be strict, with correspondingly strict processes for admittance - there will be forms to fill out in triplicate, lots of background checks, and probably an interview where the Club Secretaries grill the candidates over Martinis.
For some, this sort of club is what a federation is. But the above SAML (and SAML is of course strictly about federation so its the authority) definition for federation also allows for clubs with far less formal rules and processes and, in the extreme case, an open-door policy of everybody welcome.
There needn't even be a membership list in such a club, membership would be defined by showing up. You want in, you're in. The only rules would be to pay your money and remember to tip your bartender. I expect you'd meet some interesting people and have some great chats at such a club. Far more diversity than the 19th hole filled with leather club chairs. Probably not going to be looking for an investment banker there though.
I wonder if they validate parking.