  Difference sets and their generalisations to difference families arise from
the study of designs and many other applications. Here we give a brief survey
of some of these applications, noting in particular the diverse definitions of
difference families and the variations in priorities in constructions. We
propose a definition of disjoint difference families that encompasses these
variations and allows a comparison of the similarities and disparities. We then
focus on two constructions of disjoint difference families arising from
frequency hopping sequences and showed that they are in fact the same. We
conclude with a discussion of the notion of equivalence for frequency hopping
sequences and for disjoint difference families.
