Asyndeton is a hyponym of brachylogy.
In rhetoric|lang=en terms the difference between asyndeton and brachylogy
is that
asyndeton is (rhetoric) a stylistic scheme in which conjunctions are deliberately omitted from a series of words, phrases, clauses while
brachylogy is (rhetoric) any of several forms of omission of words, including the omission of an understood part of a phrase, as, the omission of "good" from "(good) morning!" (brachyology).
As nouns the difference between asyndeton and brachylogy
is that
asyndeton is (rhetoric) a stylistic scheme in which conjunctions are deliberately omitted from a series of words, phrases, clauses while
brachylogy is concise speech; laconism.