death vs putting to death

death and putting to death both are nouns.

Word	Noun	Adjective	Verb	Adverb
death	Yes	No	No	No
putting to death	Yes	No	No	No

As nouns, putting to death is a hypernym of death; that is, putting to death is a word with a broader meaning than death:

Other hypernyms of death include kill, killing.

death (noun)	putting to death (noun)
the act of killing	the act of terminating a life
the event of dying or departure from life
the permanent end of all life functions in an organism or part of an organism
the absence of life or state of being dead
a final state
the time when something ends
the time at which life ends; continuing until dead