ORY Hydra is the most popular OAuth 2.0 and OpenID Connect server. It integrates with every identity management and meets or exceeds security best practices.
ORY Oathkeeper is a reverse proxy which checks whether requests to your APIs should be allowed or not. No more adding isAllowed() everywhere in your code.
ORY Keto solves complex permission systems (multi-tenant, attribute-based access control, ...) with access control policies (IAM Policies).
The ORY Security Console connects with your existing ORY Hydra and ORY Oathkeeper isntallation and lets you manage and monitor them through an intuitive UI.

Auth0 is a service that abstracts how users authenticate to applications.

You can connect any application (written in any language or on any stack) to Auth0 and define its Connection, the method used to authenticate the users of that application:

Custom credentials: username + passwords
Social network logins: Google, Facebook, Twitter, and any OAuth2, OAuth1 or OpenID Connect provider
Enterprise directories: LDAP, Google Apps, Office 365, ADFS, AD, SAML-P, WS-Federation, etc.
Passwordless systems: TouchID, one time codes on SMS, or email

Running your own identity server allows you to act as an OpenID Provider. You could run one just for yourself, for a community of users or, if you wish, for the general public.