final examination vs final exam

final examination and final exam both are nouns.

Word	Noun	Adjective	Verb	Adverb
final examination	Yes	No	No	No
final exam	Yes	No	No	No

As nouns, final examination and final exam are synonyms defined as:

final examination and final exam: an examination administered at the end of an academic term

Other synonyms of final examination include final.

final examination (noun)	final exam (noun)
an examination administered at the end of an academic term	an examination administered at the end of an academic term