modern world vs modern times

modern world and modern times both are nouns.

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

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

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

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

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