neglect: omit through indifference or carelessness [ neglect to feed your gold fish/tidy your room etc] ignore: deliberately avoid something you do not want, which might get you in trouble ( ignore the speed limit)

'Ignore' means to deliberately refuse to pay attention to or notice someone or something. 'She ignored him at the party.' Neglect is not necessarily deliberate and means more to fail to care for, attend to properly or to not carry out or do something that you should do. 'The prison guard neglected his duties.'