With regards to your confusion re: "inbox apps." I will clarify and use the more appropriate terms "system and provisioned apps." 🙂
In that case, this article has misused "inbox" for "built-in" and have capitalized it for no reason too. Problem is, the above clarification only makes it worse. If I take "Inbox" (capitalized) to mean "system and provisioned apps", then why does the article make a separate category for "Common Windows 10", "Legacy Shell" and "Modern Shell" items, and more importantly, why are they treated differently. Perhaps if the article had examples, it would have been easier to understand. For example, settings created by Settings; are they legacy items, "modern" items, or common Windows 10 items?
If you are speaking specifically in developer nomenclature
Of course I'm not. I asked a practical question: Let's assume we have a LOB written in .NET Core 3.1 and package it via MSIX. Into which of your categories does it fall? Is Microsoft Edge version 82 a legacy app? What about apps packed via Desktop Bridge and sold on Microsoft Store? As I said above, examples help a lot.
Referencing this documentation, we generally classify from an app management perspective the app types on Windows 10
Now that's a good point. It is good to reference your source. The problem is that the source is talking about "different apps included in Windows 10". And sure enough, no .NET Core 3.1 app is included in Windows 10. Also not Qt apps or Electron apps are included with Windows 10 either. But Visual Studio Code, for example, is an Electron app.