Tags and categories have different connotations. To me, tags are community, collaboration, flexibility, fuzziness, visibile metadata. Categories are authority, rigidity, structure, taxonomy. Tags can be found inside content (#hashtags), categories are separate, controlling entities. Content owns tags. People own tags. Categories own content. Authority owns categories.

Beware of vague naming — some software mistakes one for the other (e.g. Mediawiki categories are in fact many-to-many).

The organisational technique used doesn’t only have technical and usability implications, but social and philosophical (or pseudo-philosophical?) ones.