According to IntelliJ:
Project:
In the IntelliJ platform, the project encapsulates all source codes, libraries, and creation instructions into a single organizational unit. Everything you do using the IntelliJ Platform SDK is done in the context of the project. A project defines collections called modules and libraries. Depending on the logical and functional requirements for the project, you can create a single-module or multi-module project.
Module:
A module is a discrete unit of functionality that can be run, tested, and debugged independently. Modules include things like source code, build scripts, unit tests, deployment descriptors, etc. In a project, each module can use a specific SDK or inherit an SDK defined at the project level (see SDK Section later in this document). The module may depend on other project modules.
Signed APK:
Signed packages for deploying and running your applications on physical devices. Based on this signature, the Android system identifies the author of each deployed application. You do not need to apply for a personal signature in any authority, a signature created by IntelliJ IDEA is sufficient.
Create APK:
In debug mode, you sign the application using the debug certificate generated by the Android SDK tools. This certificate has a private key with a known password, so you can start and debug your application without typing a password each time you make changes to your project.
Android Studio signs your application in debug mode automatically when you start or debug your project from the IDE.
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