"Primary" catalog number should be the catalog number which stores would use / appears on the spine/outer packaging.

e.g. some labels/artists apparently use an "internal" catalog number which doesn't actually appear on the release. (at least not on the outside packaging!) Editors have added these to releases anyway, e.g. from the artist's personal website, and it's now not possible to distinguish which catalog number would be "useful" to use as a search term in CD / website stores.
Exact example I had in mind is http://www.discogs.com/viewimages?release=6209 , where the "primary" catalog number should be KSC3-920, but there's an "internal" catalog number of "LPA 005 CD"

This would work best if labels were decoupled from catalog numbers, because no one wants to define whether the "primary" label is the label that (executive) produced a release or the company that marketed/distributed it.

It would also need some kind of guideline for Japanese releases where a release's "catalog number" format is dependent on how many discs are in the case. If there can only be one "primary" catno, I wouldn't mind going back to using a "non-standardized" catalog number as shown on the spine as the primary catno.