in short order vs apace

in short order and apace both are adverbs.

Word	Noun	Adjective	Verb	Adverb
in short order	No	No	No	Yes
apace	No	No	No	Yes

As adverbs, in short order and apace are synonyms defined as:

Other synonyms of in short order include chop-chop, quickly, rapidly, speedily.

in short order (adverb)	apace (adverb)
with speed	with speed
	(poetic, literary) quickly