Are desktop applications called “apps” yet?

Now that we're in a mobile-dominated world, is it acceptable to call computer programs that run on desktop computers Apps?

Take this example from the OSS Podlove subscribe button. When activated on a desktop computer, the term App is used:

screenshot of Podlove subscribe button

I had a visitor send a support request, "How do I subscribe to the podcast on my desktop computer," because they thought "App" meant it was only available for their mobile phone apps. He has a point, and I wonder if "app" is not yet appropriate for use on desktop platforms. ?

Furthermore, in this example, App is used to distinguish from Cloud, but actually the programs in the cloud are called web-apps. ?

So, what is the best terminology to use for:

  • programs on mobile?
  • programs on desktop?
  • programs on servers (e.g., MySQL)?
  • programs in the cloud (e.g., TweetDeck)?