What is the difference between an authentication provider and an identity provider.
Can Salesforce be the authentication and identity provider at the same time?
Short answer is yes. Salesforce can be Authentication Provider and Identity Provider at same time.
The main difference between Authentication Provider and Identity provider is -
Identity Provider : An identity provider is a trusted provider that lets you use single sign-on to access other websites. A service provider is a website that hosts applications. You can enable Salesforce as an identity provider and define one or more service providers. Your users can then access other applications directly from Salesforce using single sign-on.
Authentication Provider : Create a single sign-on (SSO) authentication provider to let admins and users use their non-Salesforce SSO credentials for your Salesforce orgs.
So Basically in Identity Provider your user can access Other Service (Google , Fb) from salesforce credentials where in Auth provider they can access SF using their non SF credentials.
To enable Salesforce as an identity provider:
If you want to use a CA-signed certificate instead of self-signed certificate, following these steps.
Click Save. After you enable Salesforce as an identity provider, you can define service providers by creating connected apps (From Setup, enter Apps in the Quick Find box, then select Apps).
To configure SF as Auth Provider you can follow the steps provided in link.
You can also use Salesforce as an Identity Provider for Customer Portal