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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.

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.

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