book of account vs leger

book of account and leger both are nouns.

Word	Noun	Adjective	Verb	Adverb
book of account	Yes	No	No	No
leger	Yes	No	No	No

As nouns, book of account and leger are synonyms defined as:

book of account and leger: a record in which commercial accounts are recorded

Other synonyms of book of account include account book, book, ledger.

book of account (noun)	leger (noun)
a record in which commercial accounts are recorded	a record in which commercial accounts are recorded