no-account vs no-count

no-account is a noun but no-count is not a noun.

Word	Noun	Adjective	Verb	Adverb
no-account	Yes	Yes	No	No
no-count	No	Yes	No	No

As adjectives, no-account and no-count are synonyms defined as:

Other synonyms of no-account include good-for-naught, good-for-nothing, meritless, no-good, sorry.

no-account (noun)	no-count (noun)
an idle worthless person

no-account (adjective)	no-count (adjective)
without merit; of little or no value or use	without merit; of little or no value or use