the way of the world vs the ways of the world

the way of the world and the ways of the world both are nouns.

Word	Noun	Adjective	Verb	Adverb
the way of the world	Yes	No	No	No
the ways of the world	Yes	No	No	No

As nouns, the way of the world and the ways of the world are synonyms defined as:

the way of the world and the ways of the world: the manner in which people typically behave or things typically happen

the way of the world (noun)	the ways of the world (noun)
the manner in which people typically behave or things typically happen	the manner in which people typically behave or things typically happen