What is the difference between quick apps and application builder to create an application?

The only difference is that Quick Apps is available from a special Quick Apps designer while the application builder is available directly from the Appian Designer. If you create any Quick Apps in the Quick Apps designer, those applications are also visible in the Appian Designer. However, apps created in the Appian Designer are not visible in the Quick Apps designer. The wizard steps are the same in both places and will produce the same application functionality. One other distinction is that the Application builder gives you two options: Basic and Full. Full matches the experience in the Quick Apps designer, while Basic is a more simplistic version that focuses on creating a Record Type and supporting objects.