The Authenticator app is a client application on your smartphone, usually, and you configure your profile in the cloud. I use it with my Android smartphone. 

This is a Microsoft standalone application, which the user installs usually on a mobile device, either iOS-based or in my case, Android-based. Then you add your enterprise accounts into the Microsoft Authenticator app, your work account from Microsoft 365, or your whatever on-premise account, which makes uses the Azure or whatever IDP, identity provider so that you can do single sign-on or multi-factor sign-ins.

We use the Authenticator app on our mobile phones and to authenticate for Office 365. We also provide consulting services and recommend Microsoft Authenticator to clients looking for an MFA solution.

Microsoft Authenticator is the tool provided to assure that we are using the Microsoft product in the correct way, from the Microsoft point of view.

We use Microsoft Authenticator as well as Microsoft SMS Authenticator. Normally, we enable MFA for all users who have email access and application access. Users can choose which authenticator they want to use. Based on their convenience, they enable Microsoft Authenticator or Microsoft SMS Authenticator. Almost 80% to 90% of users use Microsoft SMS Authenticator. Users who travel a lot choose Microsoft Authenticator. 

We are using the latest version. It is updated by default, and we don't have to update the application. It is also automatically updated on mobile.

My primary use case is to access our company resources. I'm a solution architect and we are customers of Authenticator.

I use Authenticator across my company for controlling access to our platforms and data.