forget vs neglect

forget is not a noun while neglect is a noun.

Word	Noun	Adjective	Verb	Adverb
forget	No	No	Yes	No
neglect	Yes	No	Yes	No

As verbs, neglect is a hypernym of forget; that is, neglect is a word with a broader meaning than forget:

Other hypernyms of forget include drop, leave out, miss, omit, overleap, overlook, pretermit.

forget (noun)	neglect (noun)
	failure to act with the prudence that a reasonable person would exercise under the same circumstances
	willful lack of care and attention
	the trait of neglecting responsibilities and lacking concern
	lack of attention and due care
	the state of something that has been unused and neglected

forget (verb)	neglect (verb)
be unable to remember	leave undone or leave out
dismiss from the mind; stop remembering	give little or no attention to
leave behind unintentionally	fail to attend to
forget to do something	fail to do something; leave something undone