An allusion is an indirect reference — a hint at something without naming it. An illusion is a false impression: something that appears other than it is. A novel makes allusions to Shakespeare; a magician creates illusions.
The core difference
One is a rhetorical device, the other a deception.
- allusion — an indirect reference: the title is an allusion to Milton.
- illusion — a false perception: an optical illusion.
The verbs
Allude goes with the first — to allude to something is to reference it indirectly. There is no verb for the second in this sense; things create or are illusions. And elude, a third similar word, means to escape or evade — a fact that eludes me.
The roots
Allusion and illusion both descend from Latin ludere, to play. An allusion plays towards something; an illusion plays against you. Elude plays away — the same root does all three.