An elusive fairy is one you can't catch, but an illusive one was never really there at all. It was just an illusion!

Anything elusive is hard to get a hold of. It eludes you. Existentialism, love, and small rodents are among things people find elusive. If you can't understand what "nothingness" is, find that special someone, or catch the little mouse who eats your cake at night, then those things are elusive. Some examples:

Predicting extreme events any further than 10 days in advance has long been an elusive goal for meteorologists. (Scientific American)

He proved an elusive foe for law enforcement. (Reuters)

Something illusive, on the other hand, is not real, even if it seems to be. The word illusive is used mostly in literature, where we find our favorite illusions. If flickering candlelight is casting scary shadows on the wall, don't worry, those are illusive villains. They aren't really there. Check out some examples from literature:

Then he knew it was an illusion of his eyes, straining suddenly in that illusive light. (Charles George Douglas Roberts)

But though all my rural visions had proved illusive, there were some very substantial realities. (Harriet Beecher Stowe)

Although both words can apply to things you don't have, don't let the difference be elusive! You can't quite catch something elusive, but illusive things are just illusions. The word illusive is less common. It likes to hang around the library, where it can be easily caught.