Hey guys, I have really thought about this and don't know the difference. Correct me if I am wrong, a link farm is a website with all links from other websites. A directory is the same just called a directory. I don't know much about this, sorry for my ignorance
I think people refer to a link farm as a site full of links, but not categorized at all. The links don't exist there for anyone's convenience, like a directory, there are only there for shady SEO purposes. More of an educated guess, so if anyone has a better definition, feel free to correct me.
A link farm is technically a system where they will link out to anyone at all who also links back to them. So you have pages full of lots of links on one site. Then you have other sites with reciprocal links back to the link farm, or alternatively pages full of a number of various links out (sometimes randomly generated from a script). That's my understanding of a link farm. If it has little or no discrimination with regard to which links are added, and requires a link or links back in return, then it's a link farm. And yes, some directories do fit the description of a link farm quite well. Those that auto-approve all sites that provide a reciprocal link back would fit the description quite closely, I believe.
I'm with Obelia. If I see a site where the pages are named "page 1", "page 2" etc then I'm out. Or the links are unthemed Or they have links to casinos, drugs, dating, scooters, moving companies (although some sites turn out ok, most aren't), cell phones Or they accept every link as submitted and make no changes to make the link fit with the style of the site. Ofcourse, even my own directories have "pages" of links but I limit them to never more than 3 and the structure and theming is all there to support the sites I list.