I am "a bit" confused in understanding of what of those two services are capable for and what are the core differences between of them.
In general, I understand what they provide, and separately I used them both earlier (VSTS as issue tracker, mostly), and AppCenter for the sources to be built and deployed.
However:
1. They both have building
and (apparently) publishing
capabilities.
In DevOps has the option of setting up the Pipeline:
Same way as AppCenter has mostly the same:
2. They both also have Tests
sections with (seems like) similar functionality.
3. They both provide ability of deploying the build into Play/App Stores.
AppCenter - with "Stores" section, and DevOps with this plugin (at least).
They both also have some specific features (like AppCenter has PushNotifications functionality and Azure DevOps has issue tracking), however, for the apps distribution they look pretty alike.
So, which of them should be used for what particular tasks? Or this is just one the modern "marketing" feature of Microsoft, when there is mostly no difference, but those are just two similar thing wrapped with different-colored envelope?