[aaronchall]

Categories are mutually exclusive.

Tags aren't. I much prefer searching in intersections of tags to searching for needles that may be in different haystacks.

[Tomte]

No, they aren't. Storage position is mutually exclusive, if you choose so, but that's not a property of categories vs. tags.

E.g. the Library of Congress assigns books to several subject headings (categories) where applicable.

[astrobe_]

Depends on what meaning you put on each word. There is no One True Meaning in this case.