Exactly how "app part" differs from apps in SharePoint 2013? Need clarification from experts on this.
An app part is one way to display information from an App for SharePoint (one of the so-called 'shapes' a SharePoint app can use).
An App for SharePoint holds all of the logic, display, and (typically) data associated with a specific piece of functionality someone has built to leverage the SharePoint framework. Apps for SharePoint are created using some flavor of visual studio (even the Napa SharePoint App) and typically added to SharePoint from an App Catalog. The actual App itself is run on a seperate domain (and sometimes a seperate server) from the main SharePoint installation; this keeps any misbehaving apps from affecting the rest of the SharePoint installation.
An app part displays an app's webpages inside of a host SharePoint site using an IFrame, that way it appears as though the contents of the app reside within the hosting SharePoint installation.
If you're interested in learning some more about App development, there is a great video series about Apps on the Microsoft Virtual Academy website; there are many different courses, but the course you might be interested in is here:http://www.microsoftvirtualacademy.com/training-courses/introduction-to-office-365-development
This link would help you more on this MSDN: SharePoint Add-ins