punting vs kicking

punting and kicking both are nouns.

Word	Noun	Adjective	Verb	Adverb
punting	Yes	No	No	No
kicking	Yes	No	No	No

As nouns, kicking is a hypernym of punting; that is, kicking is a word with a broader meaning than punting:

punting: (football) a kick in which the football is dropped from the hands and kicked before it touches the ground
kicking: the act of delivering a blow with the foot

Other hypernyms of punting include boot, kick.

punting (noun)	kicking (noun)
(football) a kick in which the football is dropped from the hands and kicked before it touches the ground	the act of delivering a blow with the foot
	a rhythmic thrusting movement of the legs as in swimming or calisthenics