commutation vs commute

commutation and commute both are nouns.

Word	Noun	Adjective	Verb	Adverb
commutation	Yes	No	No	No
commute	Yes	No	Yes	No

commutation (noun)	commute (noun)
the travel of a commuter	a regular journey of some distance to and from your place of work
(law) the reduction in severity of a punishment imposed by law
the act of putting one thing or person in the place of another:
a warrant substituting a lesser punishment for a greater one

commutation (verb)	commute (verb)
	change the order or arrangement of
	exchange a penalty for a less severe one
	exchange or replace with another, usually of the same kind or category
	exchange positions without a change in value
	travel back and forth regularly, as between one's place of work and home