Apple Business Manager is used by organisations to deploy Apple devices and obtain both App Store apps and B2B apps using the Volume Purchase Program:
Apple Business Manager is a simple, web-based portal for IT administrators to deploy iOS, macOS and tvOS devices all from one place. When used with your mobile device management (MDM) solution, you can configure device settings and buy and distribute apps and books.
The Enterprise Developer Program allows organisations to develop and distribute apps to their own devices without uploading them to the App Store and without going through Apple App Store review:
Distribute proprietary, in-house iOS, watchOS, and tvOS apps within your organization. Securely host and deploy apps to your employees' devices.
You do not need have an Apple Enterprise Developer Program membership to use Apple Business Manager.
In summary:
- You would choose Apple Business Manager if you want to manage devices using the Device Enrolment Program and to obtain apps developed by others using VPP
- You would choose the Enterprise Developer Program if you want to develop apps for in-house use that are not suitable for the App Store or should not be available on the App Store.
You would use one or the other or both depending on your needs.
Update
Apple now allows organisations to "sell" B2B apps to themselves; This means that in many cases a B2B app can be used in place of an Enterprise app. Enterprise apps require periodic refresh of their provisioning profiles and certificates and also need Internet access to verify their signatures. Unless you are creating an app that will not pass Apple review (e.g. private API use), Apple now recommends B2B apps over enterprise program apps.