augment vs increase

augment is not a noun while increase is a noun.

Word	Noun	Adjective	Verb	Adverb
augment	No	No	Yes	No
increase	Yes	No	Yes	No

As verbs, increase is a hypernym of augment; that is, increase is a word with a broader meaning than augment:

augment (noun)	increase (noun)
	the act of increasing something
	the amount by which something increases
	a change resulting in an increase
	a process of becoming larger or longer or more numerous or more important
	a quantity that is added

augment (verb)	increase (verb)
grow or intensify	become bigger or greater in amount
enlarge or increase	make bigger or more