presence of mind vs willpower

presence of mind and willpower both are nouns.

Word	Noun	Adjective	Verb	Adverb
presence of mind	Yes	No	No	No
willpower	Yes	No	No	No

As nouns, willpower is a hypernym of presence of mind; that is, willpower is a word with a broader meaning than presence of mind:

presence of mind: self-control in a crisis; ability to say or do the right thing in an emergency
willpower: the trait of resolutely controlling your own behavior

Other hypernyms of presence of mind include possession, self-command, self-control, self-possession, self-will, will power.

presence of mind (noun)	willpower (noun)
self-control in a crisis; ability to say or do the right thing in an emergency	the trait of resolutely controlling your own behavior