Well Emacs can almost but not quite be everything of course.
But this is a pretty common distinction, surely?
Words are text, but word processors have historically been focused on preparing documents for printing (or nowdays viewing a visual representation of a printed document onscreen, eg PDF).
They handle differing visual layout (fonts, page breaks, margins, indenting). They are softwrapped and paragraph based not line based. Often they deal with formatting through styles - headers, bullet points, numbering. They usually handle inclusion of tables, images and other non-text elements.
The most common example of a word processor, Word, also handles collaborative writing with tracked changes and notes, and has inbuilt features such as on the fly word count, spelling and grammar checks.
As I said, for a command line word processor look at WordPerfect for DOS or equivalent.
What you are saying (and it is not entirely wrong) is that you can approximate a word processor by matching a text editor with a bunch of other programs (TeX, Pandoc, aspell etc). But that doesn't make the text editor a word processor.