There are two ways of treating conferences that are commonly mentioned on this site:
Conferences are publication venues for papers (or similar). Submissions will be subjected to a serious peer review, are citable as evidence, and are a relevant achievement. Submitting the same material to two different conferences or a journal and a conference would be considered self-plagiarism.
This applies to computer science and engineering (or at least some subfields thereof) – for details, see: Is the status of conference publications in Computer Science really absolutely unique?
Conferences are not publication venues. The material presented there is typically also published in journals, books, and similar – but this process is not tied to the conference; it may occur before the conference, later, or even not at all. Submissions are only subjected to minimal review¹, are not citable as evidence, and not considered a big achievement. Participating in conferences is still considered important though. It is common that authors present the same material at different conferences.
This applies to the majority of fields.
¹ to weed out utter crap or to decide what should be a talk and what a poster
In light of this Meta question, I am interested whether the above two cases are the only two. To me, it would not be surprising if this actually is the case, as the two categories have a self-preserving mechanisms. For example, for a conference belonging to the first category, weakening the criteria for submission would usually be a bad move. On the other hand, I am very well aware that I do not know every field’s customs. Hence, I am asking: Are there conferences that hold a status not described by the two categories above? Please answer only if you can name and describe such a conference – if this question remains unanswered, this would be an acceptable and meaningful outcome.
Note that this is only about what is submitted directly to the conference for the purpose of being presented there. Whether articles corresponding to the presented material will be collected for a book, special issue of a journal, or other form of proceedings – be it with separate peer review or not – is irrelevant for the purposes of this question.