nervii olfactorii vs first cranial nerve

nervii olfactorii and first cranial nerve both are nouns.

Word	Noun	Adjective	Verb	Adverb
nervii olfactorii	Yes	No	No	No
first cranial nerve	Yes	No	No	No

As nouns, nervii olfactorii and first cranial nerve are synonyms defined as:

nervii olfactorii and first cranial nerve: a collective term for numerous olfactory filaments in the nasal mucosa

Other synonyms of nervii olfactorii include olfactory nerve.

nervii olfactorii (noun)	first cranial nerve (noun)
a collective term for numerous olfactory filaments in the nasal mucosa	a collective term for numerous olfactory filaments in the nasal mucosa