I think the difference is in persisting in belief even after it has been proven not to be so. If you think one of your teeth contains a receiver or transmitter from the CIA and that tooth is taken out and opened up/broken apart and none is found but you still say it is there, that is a delusion. Thinking you see a ghost (which, being a ghost it "disappears") it can't be proven whether or not it was there so that can be a hallucination. Someone here was hallucinating cats in restaurants, for example. She knew they were hallucinations but some others might believe they are real cats but since it couldn't be proved something wasn't there in the past that isn't there anymore now, that would be a hallucination. I think hallucinations are more about what was seen/heard/other sense rather than one's belief about what was seen/heard/other sense, which would be delusion.

Brina had the belief as a child that there was a black dog under her bed and that belief is what made her afraid to get out of bed. No one showing her that there wasn't a black dog could influence her belief. If she'd seen a black dog under her bed and now it was gone and she could get get out of bed, that would be hallucination but the belief the dog was there, when it was shown to her that it wasn't is delusion.