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There is a standard, Panose, but it is mostly ignored by typographers (not because it's bad, just because they don't need it). The Panose system is documented, among other places, in the Microsoft Windows 3.1 Programmer's Reference from Microsoft Press.
The ISO also has a scheme, but it is not Panose.
At least one book by a respected authority, Alexander Lawson, Printing Types: An Introduction, describes another, less rigorous system [ed: of his own], which is exposited in ``An Introduction'' and used without exposition in his later ``Anatomy of a Typeface''.
There is another book, Rookledges International Typefinder, which has a very complete system that uses tell-tales of individual glyphs as well as overall style to index most known faces right in the book.
J. Ben Leiberman has another book on type face description.
Terry O'Donnell adds the following comments:
The current ISO system was initiated (I believe) by Archie Provan of RIT---a successor to Mr. Lawson. Whereas in typographic practice or teaching---only a high level classification is necessary - times have changed and the current ISO system aims to accomplish something beyond the high level. A major goal is to aid software to help users make selections. For example, a naive user might ask for all fonts on a font server which have a Roman old style appearance. Another goal would be to help users with multi-lingual text: a user creating a document in English using e.g. Baskerville wants to know what Arabic or Japanese language font on his system/file server would harmonize well with the Baskerville. It is not all in place yet---but the more detailed ISO classes---and the current addition of non-latin typefaces---are an attempt to address this issue.
A second goal is to help with the font substitution problem. Neither ISO or Panose address the metrics issues in font substitution---but both might aid software in picking the nearest style of available available fonts.