apace vs in short order

apace and in short order both are adverbs.

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

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

Other synonyms of apace include chop-chop, quickly, rapidly, speedily.

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