What exactly is a “Book App”? How is it different from an “eBook”?

A "Book App" is an interactive, animated app that either tells a story or provides useful information.  The keyword here is "interactive", meaning it engages the reader(s) by presenting opportunities to tap on characters, props, or "hotspots", which respond to the tap with one or more sounds, animations, videos, links to other reactive functionality within the app, or a chain of events such as having the book app read itself to you while highlighting words, etc.

In addition to interactive pages, Book apps can also contain puzzles, activities, games, quizzes, coloring pages and other interactive features.

An eBook is simply an "electronic book".  it is essentially an electronic version of a page-turning physical book that you simply read.  Some eBooks may include a few simple bells and whistles, but a richer interactive experience requires the infrastructure provided by a book app.