To make matters more complicated, we also have documentation.
It's all very confusing, admittedly. I think we can remove books in favour of manuals (there are only 10 questions marked with books, and those can be retagged painlessly a few at a time in the course of several days), and keep the rest as they are.
The documentation tag is applied somewhat inconsistently currently, I'd imagine it to be mostly about package documents (hah!) that describe in detail provided commands, available options, behaviour and implementation details, most likely including source code.
float package, TikZ-pgf manual.
manuals is a good tag for any sort of higher-level user guide to a certain broader topic (e.g. typesetting mathematics, a TeX-derivative, or general introductory material), without describing every package, tool and command under the sun.
Examples: The TeX Book, The Not So Short Introduction to LaTeX, or ConTeXt, an excursion.
When I noticed the ambiguity of the books tag, I created the book-design tag for the sake of clarity. Further I talked about that in the tag wiki. I think that's sufficient, at least if we would correct a misused tag from time to time.
books is just a fine tag for books about TeX, LaTeX and related software, brief and concise.
I think documentation is good to refer for general documentation, most notably electronic documentation such as package manuals, not as good for real books which might be distinguished.