Why does an app have a different icon on my actual phone vs on Bluestacks and its Desktop Icon? Why does an app have a different icon on my actual phone vs on Bluestacks and its Desktop Icon?

The icons do work, and are related to the app they're for.

The app is "Eternal Senia: Hydrangea after the Rain".

It's free, so you can check for yourself if you want.

The icon on my phone is Senia's head, while the one for Bluestacks is Rita's.
There are two main reasons why an app shows a different icon:


Some apps provide different APK files for different platforms. Different APK files means that of course not only the code but also resources like images can be different. However it seems like the app you mention is only available in one version.
An app contains images and icons for different device resolutions. Therefore if the display pixel density (measured in dots per inch - dpi) of your actual phone and the Bluestacks VM differs you may see different images. How much they differ depends on what images has been created by the app developer.