modern world vs present times

modern world and present times both are nouns.

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

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

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

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

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