miter box vs mitre box

miter box and mitre box both are nouns.

Word	Noun	Adjective	Verb	Adverb
miter box	Yes	No	No	No
mitre box	Yes	No	No	No

As nouns, miter box and mitre box are synonyms defined as:

miter box and mitre box: hand tool for guiding handsaws in making crosscuts or miter joints

miter box (noun)	mitre box (noun)
hand tool for guiding handsaws in making crosscuts or miter joints	hand tool for guiding handsaws in making crosscuts or miter joints