Microsof ADFS supports below federation protocols:
Would like to know is it possible to achieve single sign on (SSO) and single logout across different protocols? E.g. user X after he/she successfully login to website A which is protected under SAML 2.0, then the user can access website B which is protected under OpenID Connect without re-login? Both website A and website B point to the same IdP.
There are typically the parties involved. Of these, website B is the modern architecture and can support many forms of authentication:
Single Sign On is represented by a third party session cookie issued for the SAML IDP's domain name. Both apps would redirect to the SAML IDP but only the first would result in a login prompt. Website B may need to send the acr_values OpenID Connect parameter during its redirect, to avoid the user being presented with an authentication selection screen. It should work fine, but test for your providers. The SSO cookie is maintained in current browsers on the second redirect, due to the user gesture of a top level redirect.
Single Sign Out has always been a set of draft standards that work imperfectly in all of the above protocols. Even if the technology works, there would be risks such as also signing the user out of App C, which you do not own. Also, recent browser restrictions on third party cookies mean some techniques may drop the SSO cookie and no longer work. Most stakeholders, including end users and security reviewers, do not expect you to have a perfect Single Logout solution.