Hmm, interesting question. They are somewhat similar, but there are definite differences.
In my opinion:
Illusions: Anything that one perceives as true but is not. This can cover optical illusions, mental illusions, etc. etc. i.e. either your senses or intellect are fooled/tricked, frequently because of confusing input. As an example, magicians are sometimes called illusionists because they make us think we see things that aren't really happening.
Delusions: Somewhat like illusions, but they are more self-directed/self-willed/self-inflicted. i.e., they are things we wish were true, so we imagine that they are true. For example, the expression 'delusions of grandeur' refers to a person thinking they are more important than they really are. Examples of delusion might include a person imagining that a famous movie star is going to marry them, imagining they will win the lottery, imagining they will become a world-famous celebrity, etc. Or it could be something as simple as ignoring all the signs that their boyfriend is cheating on them, when it is obvious to everyone else.
Hope that helps.