old age vs decrepitude

old age and decrepitude both are nouns.

Word	Noun	Adjective	Verb	Adverb
old age	Yes	No	No	No
decrepitude	Yes	No	No	No

As nouns, decrepitude is a hyponym of old age; that is, decrepitude is a word with a more specific, narrower meaning than old age:

old age: a late time of life
decrepitude: The quality or state of being wasted and weakened by or as if by the infirmities of old age.

Other hyponyms of old age include dotage, second childhood, senility, autumn years.

old age (noun)	decrepitude (noun)
a late time of life	a state of deterioration due to old age or long use
	The quality or state of being wasted and weakened by or as if by the infirmities of old age.