presence of mind vs self-will

presence of mind and self-will both are nouns.

Word	Noun	Adjective	Verb	Adverb
presence of mind	Yes	No	No	No
self-will	Yes	No	No	No

As nouns, self-will is a hypernym of presence of mind; that is, self-will 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
self-will: the trait of resolutely controlling your own behavior

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

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