I am assuming you mean ATA vs AATP (MDI).
Functionally the products do the same concept.
ATA is "on prem" in the sense that in additionally to deploying an agent on the DC, you also deploy the "center" that holds all the data on your own.
It's also the older product that is no longer actively developed (switching to extended support on Jan 21).
For AATP (MDI) you just need to install the sensor services on the DC (instead of the ATA Gateway services) and Microsoft gives you the "Center" hosting in Azure.
This product is actively developed, and at this point also offers much more features compared to the older ATA.
As for migration, it's normally uninstalling the Gateway services, and installing the sensor services instead.
There is no auto migration, it's advised to take note of any settings you had in the ATA console (like exclusions, AD credentials, notification rules, reports etc)
And manually apply them in AATP Portal.
Eventually, both products protect on prem domain controllers.