Capitalization of App

I'm trying to write a promotional piece on our new app. I can't figure out how to capitalize in these two instances (not in a title). My gut tells me lowercase but other team members have been using capital A. What's the reasoning behind the correct answer?

Welcome to the new XYZ App/app. Our App/app has many new features.

Whether to capitalize the first case depends on whether you consider app to be part of the title of the product. If you call your program XYZ App, as opposed to XYZ, then App would be correct. Otherwise, if your product is simply titled XYZ, then app is appropriate.

In the second case, app is preferred. The word app is short for application, so it would be weird in most contexts to capitalize it. (Exceptions exist, as always.)