  Classical strong external difference families (SEDFs) are much-studied
combinatorial structures motivated by information security applications; it is
conjectured that only one classical abelian SEDF exists with more than two
sets. Recently, non-disjoint SEDFs were introduced; it was shown that families
of these exist with arbitrarily many sets. We present constructions for both
classical and non-disjoint SEDFs, which encompass all known non-cyclotomic
examples for either type (plus many new examples) using a sequence-based
framework. Moreover, we introduce a range of new external difference structures
(allowing set-sizes to vary, and sets to be replaced by multisets) in both the
classical and non-disjoint case, and show how these may be applied to various
communications applications.
