I received a very helpful clarification after emailing ENCODE directly:
Nuclease accessible regions tend to be long, e.g. 10 kb or longer.
This was clear even in the early papers on DNase sensitivity
(mid-to-late 1970's; Groudine and Weintraub). These accessible regions
can contain entire genes or even clusters of genes. Within the
nuclease accessible regions, some localized DNA segments are so
readily cleaved that double-strand breaks are generated at that
position in a substantial fraction of the cells in the population.
These are the DNase-hypersensitive sites (DHSs) first mapped by Carl
Wu (late 1970's). I see the Fseq "regions" as the equivalent of
nuclease accessible regions, and the Homer "peals" as the equivalent
If you look at the signal track for DNase-seq or ATAC-seq, you see
broad regions of signal that are significantly above the background.
Within those regions, you see localized peaks, often many peaks per
region. Fseq calls the broad regions, and we use Homer to call the
localized peaks. MACs can be used for peak calling as well, Anshul
Kundaje is doing that. You can see similar analyses in the work from
John Stamatoyannopoulos for DNase-seq. I think Hotspots are like
regions, and DHSs are peaks confined to a defined length.