An illusion is not real; so someone may have a false idea or see something that isn’t really there – they are facing an illusion.

Allusion is a reference to knowledge you assume your reader/listener understands, especially when referring to literary or art knowledge. For instance, I will make an allusion to Shakespeare’s work when I write: the young couple considered themselves to be as tragic as Romeo and Juliet. I can assume that most people know the story of Romeo and Juliet so the allusion explains a lot in few words.

To remember which is which, consider that illusion starts with I and often relates to a trick of the eye. Allusion starts with A and usually relates to Art and literature.