present times vs contemporary world

present times and contemporary world both are nouns.

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

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

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

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

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