What's the difference between paranoia and delusions?

Sometimes degree. Delusions are things a person believes despite evidence to the contrary. Paranoia can be a type of delusion and in that case may not respond to treatment. However, the feeling of paranoia can be treated.
They can be related. Paranoia involves being suspicious and this often leads to being fearful. Delusions are defined as fixed false beliefs. Often if you are paranoid and suspicious of someone this is followed by a delusional belief. Paranoia and delusions can occur in many different illnesses, not just schizophrenia.