nihil obstat vs imprimatur

nihil obstat and imprimatur both are nouns.

Word	Noun	Adjective	Verb	Adverb
nihil obstat	Yes	No	No	No
imprimatur	Yes	No	No	No

As nouns, imprimatur is a hypernym of nihil obstat; that is, imprimatur is a word with a broader meaning than nihil obstat:

nihil obstat: the phrase used by the official censor of the Roman Catholic Church to say that a publication has been examined and contains nothing offensive to the church
imprimatur: formal and explicit approval

Other hypernyms of nihil obstat include countenance, endorsement, indorsement, sanction, warrant.

nihil obstat (noun)	imprimatur (noun)
authoritative approval	formal and explicit approval
the phrase used by the official censor of the Roman Catholic Church to say that a publication has been examined and contains nothing offensive to the church