The relevant guideline, which is visible on the form used to suggest a URL for inclusion in the Directory, is:
Multiple submissions of the same or related sites may result in the exclusion and/or deletion of those and all affiliated sites.
But what does this really mean?
Multiple means more than once. Suggest an URL once to the best fit category you can find. An editor will move it to another category if you have got it wrong. If they think it is suitable for more than one listing they will also often send a copy of the URL to another category for consideration.
The "same sites" takes two meanings. Either the exact same URL or the same site using a different URL, a mirror. Same is also broader than identical in every respect - rehashing words, applying a different template design, or rearranging the menus does not make it different, and it will still be treated as a mirror site.
The meaning of "related sites" is the one that causes most difficulty. Webmasters tend to take a very narrow view and intepret it the same as a mirror. Editors take a broad view.
Related, from an editor's perspective, means a business that markets/sells related services and products, but elects to market them on separate websites. Web hosting, web design, content management, domain names, etc. etc. are all (for DMOZ purposes) related products and services. If there are 4 websites belonging to the same business selling each of these products separately, editors will only list one of those sites. Otherwise Business A would get 4 listings because they have put up separate sites for each services, when Business B gets 1 listing because all their services are on the same site. In fact, Business A is risking getting no listings at all because spreading their content too thin may actually leave each site with insufficient content for a listing. Business in this context is taken to be the entire business portfolio of a particular entity regardless of tax and legal corporate distinctions.
So we are talking related in terms of content AND beneficiary (owner/operator/etc.)
Sites that are related in terms of content only will almost certainly fall foul of other provisions such as lack of original content, affiliate, etc.
Sites that are related *only* in terms of beneficiary are not subject to rejection on those grounds alone, though many fall at other hurdles.
Examples:
Andy owns a web design site, Ben owns a web design site, they are direct competitors, both may be listed subject to having sufficient original content, even though they are both selling more or less identical services.
Carl owns a web design site and a web hosting site. They are selling related services (web services) for Carls benefit. David, his nearest competitor, owns a site selling web design and hosting services on the same site. Carl and David are entitled to one listing each, subject to having sufficient original content.
Ernie owns a web design site and another selling teapots. These are entirely different business areas and even though the sites may have reciprocal links each would probably be considered independently.
Frank owns a site selling retail teapots, and another selling wholesale coffee. Very careful consideration would be given as to whether to treat them as related or separately. Each site would be scrutinised very carefully and maybe several editors would get involved.
Gary cuts a deal with Frank and becomes a reseller of Frank's teapots. Frank rehashes the content of his site and gives it to Gary as part of the deal. DMOZ won't list Gary's site - it lacks original content.
The more clear cut the lack of a relationship between the content: teapots, web design, etc. the easier the decision to treat them independently. The same the other way around, the closer the relationship the easier to make a decision to treat them as related. From Internet, the circle of "related" may well extend into all things technological - telephony, hardware, networking, etc.
But you also hit a point where a business is so diverse: teapots, tennis balls, computers, furniture, that editors would look at them as general merchandisers.
[Don't worry I cut and pasted that from elsewhere, I'm not that quick a writer or that long-winded.]