the ways of the world vs the way of the world

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

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

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

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

the ways of the world (noun)	the way 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