unbounded interval vs open interval

unbounded interval and open interval both are nouns.

Word	Noun	Adjective	Verb	Adverb
unbounded interval	Yes	No	No	No
open interval	Yes	No	No	No

As nouns, unbounded interval and open interval are synonyms defined as:

unbounded interval and open interval: an interval that does not include its endpoints

unbounded interval (noun)	open interval (noun)
an interval that does not include its endpoints	an interval that does not include its endpoints