"Hate" is not really a noun. It's a verb. The noun is "hatred" although "hate" is increasingly being used as a noun.
Hate is a noun - there's no 'not really' involved. I can't think of any difference in meaning to 'hatred' (the Oxford English Dictionary gives both as mass nouns meaning 'intense dislike') but would be interested if someone could tell me a difference.
To add to the above, you can also say 'hatred towards' - 'I don't feel any hatred towards him anymore; I've learnt to accept him for what he is.'