There aren’t two different things like app and apk from Android’s context
App is a Application that as a whole presents a group of services and features provided by app whereas apk is extension of android app i.e android app files have .apk extension like music have .mp3
Hence when you install app you install apk and vice versa
This is my take on the answer.
An APK file is an app in its installable form. It contains anything needed for the installed app to run, such as code, graphic resources and so on. It is basically a ZIP archive, signed by its developer.
An app is a rather complicated concept: when one installs an APK file via a special software known as a Package Installer, certain of the file’s contents are extracted, such as the libraries.
The .dex file or files contained within, being what makes the app work, are optimized for Dalvik or ART, which is the Android component in charge of running an installed app.
Additional procedures such as the creation of the app’s data directories and its declaration in a special file known as the
packages.xml occur as well. This file is used by Android in order to know which apps are installed, where their APK file is located and what permissions are in use by them.
Knowing where the APK is located is important, because Android keeps a copy of the original APK file, from where it loads an app’s necessary resources, if they have not been loaded into a special cache yet. This means, that an APK file is vital to an app.