Is a user provider and an identity provider the same thing? If not what are the differences and where would you typically specify a user provider in an email notification set up?
Typo. "user source" is the correct terminology. This is a classic feature of Ignition where all authentication and role assignments are performed by the Ignition gateway, with a number of backend technologies (internal, database, active directory) and some ability to chain.
"Identity Provider" is the modern feature of Ignition where authentication and roles are delegated to a web-based, standardized API. Ignition comes with its own identity provider implementation that points at any classic user source.
Ignition's user management tools rely on Ignition's control over users and roles through a classic user source. Standardized web authentication APIs do not expose user management.
In alarm notification rosters. These are drawn from user sources, and are where Ignition obtains the target email addresses to be used. These have no relation to configuring how Ignition delivers email to an SMTP server.