Your definition of link far is accurate, creating a directory as part of your site (which is rich in contents) does not turn it to link farm, link farms tends to have link only and they link to almost any site.

A link farm in the traditional meaning was a page or site that was duplicated across a set of sites, and, everytime a new site was added and that new site uploaded the code, everyones site got his link. The term farm came because everyone seeded the directory and they ALL harvested when new members joined. Such schemes still exist today, and in fact are mail marketed and pushed through forums on a regular basis. They use headlines like ' get hundreds of backlinks to your site instantly' etc.

The first instance you give is more of a Free for all (FFA) page, which again is frowned on by google.

The option you have for your directory is not wrong in any way, and would enhance the visitor experience. Can I suggest though that you add the 'posts anywhere' mod to your forum and display them on the directory, and also add backlinks from the directory to the best forum area for that cat? RSS could achieve this with ease.