How can I authenticate for one ServiceProvider site, and then no authentication needed for different ServiceProvider sites?

We use ADFS 2.0 to access ServiceProvider sites.  If I go to the ServiceProviderSite#1(SPI), it will redirect me to ADFS and I authenticate and then get connected into that site.  That works fine and I thought the token that was issued, was always embedded into the cookie for that specific website.  However, I do notice that if I go to a different ServiceProvider site I go right through, without any authentication.  It knows I have already authenticated to ServiceProviderSite#1.  My guess is that it picked up on the token that was issued to me for ServiceProviderSite#1.  Does anyone know how that works?

Thanks,

Dan

Dan Heim