Hi Ved,
>> My doubt is what data - session info/session identifier, do I need to transfer(perhaps as a query param) from first service provider (Site-A) to the second service provider(Site-B), so that Gluu knows that user has already been logged on (and there by user does not have to login again) and it returns the SAML reponse to Site-B as per its metadata.
No, you don't need to transfer anything by yourself if you are using same browser ( different tab ) for various SPs. 2nd, 3rd, 4th login will happen automatically without asking for credential.