What is an out-of-band authenticator, and what is push authentication?
An out-of-band authenticator is an authentication means that uses a separate, independent communication channel in addition to the primary authentication request: a uniquely addressable physical device in the subject's possession that can receive single-use secrets; a push message is a short notification sent by a service to the subject's mobile device that the subject confirms by tapping or swiping, usable as second factor in MFA.
Two modes exist: the subject types the secret received over the second channel into the primary channel, or answers directly over the second channel. Examples: SMS code, push notification, verification call to a registered number. Push messages travel via APNs (iOS) or FCM (Android).
Go deeper:
NIST SP 800-63B-4 Authentication and Authenticator Management โ every authenticator type defined and graded by assurance level.