I might illustrate with these two characters:
1) One alcoholic will not stop drinking and driving - he says "I don't have a problem, and I'm not hurting anyone."
2) A second alcoholic has stopped drinking, because he believes that doing so will improve his life, and keep him from hurting himself and others.
One of the two is in denial, the other is acting on hope.
Perhaps the one in denial is right, and he never will hurt anyone... but he hasn't stopped putting others at risk, and he hasn't acknowledged that his actions are putting others at risk. Whether he is correct or incorrect, he is still in denial.
And perhaps the one who is acting on hope is wrong, and even though he has stopped drinking he ends up in a car accident and hurts someone anyway, or he finds out he has cancer and his life does not improve significantly. Whether his hope is fulfilled or disappointed, he still has hope that doing what is right will turn out for the best.