What is the difference between MDM and third party services for distributing the app from Enterprise Developer Program?
Mobile Device Management (MDM) or Mobile Application Management (MAM) solutions can be used to distribute in-house apps to the employees. For this, they'll need to enroll the employees' devices in MDM or MAM. After this, they can upload in-house apps to the MDM console and bulk push to the enrolled devices. It is also possible to distribute apps that are in the App Store.

Can you make it clear what you told about TestFlight, as I didn't catch it? You said "He wants the feature like TestFlight", but TestFlight is an independent service (MDM do not come with TestFlight). Head on to the section 'TestFlight Beta Testing' in this article and you'll learn more about it.

The app that distributed through TestFlight is the 'beta app' which have a life of 60 days for each build. On the other hand, 'in-house apps' have an infinite lifetime.

If you need to know anything from me, leave a comment. I am happy to help.