"Intergenic" is, well, an embarrassment, though it can be hard to avoid. Intergenic means, literally, between genes. Genes are, as you'd expect, genetically defined as regions of the chromosome with some genetic role. Between genes, we have, well, junk, spam, without meaning or significance, since otherwise, it would be a gene. In the 1990s everybody knew most of the genome was "junk DNA" and it was pretty straightforward. And the central dogma was DNA makes mRNA makes protein and if there was no mRNA making protein, or even no long protein, then they assumed there was no gene.
Well, the problem with using these terms nowadays is, first, it is very hard to show any given piece of DNA never has a role. After all, you can often remove a whole gene without visible effect on an organism, so how can some noncoding sequence 'between genes' be proved conclusively to be meaningless and of no relevance to either of its neighbors? And second, DNA definitely does have a role even if all it does is produce non-coding RNA, or act as a regulatory sequence that does. So for example, on OMIM you can look up many records for "intergenic", with results like H19, for which one term is "LONG INTERGENIC NONCODING RNA H19". Note also H19 is listed as the HGNC approved gene symbol, so it is an intergenic gene. Tricky, eh? (I have great respect for OMIM - this isn't their fault) Also, enhancers can be quite a long way from a gene, even past the end of another gene or affecting multiple genes, so even though a mutation in the enhancer might genetically act as an allele of a specific gene, it might be described in sequence terms as located in an intergenic region.
Bottom line: the intergenic regions you're reading about are going to be between things that are recognized as genes, and may or may not be known to have some effect on one or the other (or both...). They won't contain CDS, which is always considered to be a gene, nor 5'UTR or 3'UTR because those are transcribed before or after a CDS. Past that, how they are being distinguished from "upstream sequence" and "downstream sequence", that could be completely arbitrary. They might have gone to WormBase and pulled out curated gene records, and added some number of base pairs before the start site as promoter - but I don't know that. You'll just have to try to find the particular reference for whatever tool you are using.