To copy Styles from one document to another or to a template when Styles of those names exist in the destination file, you should use the Organizer (Tools>Templates and Add-Ins>Organizer).

To update the Styles of a document for which they've been updated in its template, go to Tools>Templates and Add-Ins, then check the option to 'Automatically update document styles'.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]