I think the key is not so much the on-screen presentation but the file layout. Typically, TextEditors put only the text you typed into the document. No additional formatting, meta data, etc. This is a direct consequence of the fact that TextEditors grew out of the need to provide input to compilers and interpreters for computer languages. These tools operate on basically pure text.
I am careful not to identify what that is because it depends somewhat on platforms. For example, on mainframe operating systems, there are fixed length and variable length files with no line terminating characters. However, the end of line is identifiable.
I agree with Ron. To understand the difference between text editors and word processors, consider how text editors differ from three well-known word processors: WordStar, WordPerfect, and MicrosoftWord. For example, WordStar had a "nondocument mode" which produced flat ASCII text suitable for programming source code. However, it also had a "document mode" in which the last character of every word had the 8th bit set, and the user could embed no less than 16 different control characters (QWERTYASDGHOPVBN) directly into the file to control the print format: bold, double-strike, 10cpi, 12cpi, underline, italics, proportional spacing, etc. Word processors like Word Perfect and Word also embedded many other hex and control codes for headers, footers, footnotes, endnotes, tables of contents, words-to-be-indexed, two- and three-column formatting, inserted graphics, non-English characters and symbols, images, and much more.
To me, the simple test of the difference between a text editor and a word processor is the file format. If your text consists solely of "Hello, world!", and you type the file the screen, does it look normal? Word processors add metadata to the file (owner, printer driver information, etc.) and text editors do not. For additional perspective, see the WordProcessor wiki entry. -- EricPement
Therefor, word processors are essentially text editors with additional features for controlling the appearance of the end result.
Most word processors combine text creation/editing and output formatting features in the same program, but it's also possible to split them out. Unix did that 25 years ago, where the implicit assumption was that you would create your text in the vi editor, and then format it for printing with something like nroff. The disadvantage to that approach is that the user must learn a markup language, and embedded the markup commands in the text before printing. Modern word processors embed the markup code as meta data in the document, that is not displayed directly, but rather by its effects, as type can appear as bold face, italicized, or underlined, in different fonts, colors, and sizes. --DMcCunney
One weakness of text editors is that plain ASCII does not provide an easy way to handle auto-numbered footnotes or endnotes, which are often required in an academic setting. I attend one school and work at another school, and footnotes or reference documentation is very important here. I developed scripts in perl and awk to handle EndNotes in ASCII text. This lets users add, delete, move, or rearrange note references in an ASCII document, and then have the note references collected and moved to the end, with everything auto-numbered whenever they want.
Rather than describe it all here, I think the best way is to [look here] at my sample input and output text, and if interested, get the corresponding code for either [awk] or [perl]. The neat thing is, this system works with any text editor, and it's an easy, low-pain solution to a long-standing problem. I only wish I thought of it first. (smile) -- EricPement
At school, I used the formatter that came with BlackBeard editor (I'm thinking it was called BBFMT.EXE or something).