contemporary world vs modern times

contemporary world and modern times both are nouns.

Word	Noun	Adjective	Verb	Adverb
contemporary world	Yes	No	No	No
modern times	Yes	No	No	No

As nouns, contemporary world and modern times are synonyms defined as:

contemporary world and modern times: the circumstances and ideas of the present age

Other synonyms of contemporary world include modern world, present times.

contemporary world (noun)	modern times (noun)
the circumstances and ideas of the present age	the circumstances and ideas of the present age