delusion: The free dictionary: 1. a. The act or process of deluding. b. The state of being deluded.
2. A false belief or opinion: labored under the delusion that success was at hand. 3. Psychiatry A false belief strongly held in spite of invalidating evidence, especially as a symptom of mental illness: delusions of persecution.
Cambridge dictionary: when someone believes something that is not true
mirage: The free dictionary: 1. An optical phenomenon that creates the illusion of water, often with inverted reflections of distant objects, and results from distortion of light by alternate layers of hot and cool air. Also called fata morgana. 2. Something illusory or insubstantial.
Cambridge dictionary: an image, produced by very hot air, of something which seems to be far away but does not really exist __________________________________________________ _____
In conclusion... they are not very different from each other. Similar, yes, synonyms, I don't think so.