Their comparison to and discussion of the iPhone behaviour seems to be quite disingenuous to me: The iPhone search searches websites and your phone. Apps that you have installed on your phone can register to provide search results.

If you don't have Apple Podcasts installed, you won't get any search results for "Apple Podcasts" (I tested this). And if you have another podcast player installed that supports iPhone-wide search (e.g. Overcast), you will get search results from that other podcast player.

This seems to me to be quite different from the Google search, which (from what I understand from the articles) always seems to link to Google Podcasts if you are using it on Android.