Delusion, illusion, hallucination, mirage denote something which is believed to be or is accepted as being true or real but which is actually false or unreal.
Delusion in general implies self-deception or deception by others; it may connote a disordered state of mind, extreme gullibility, or merely an inability to distinguish between what only seems to be and what actually is true or real.
Illusion seldom implies mental derangement or even the inability to distinguish between the true and the false; rather it implies an ascription of truth or reality to what only seems to be true or real, especially to the eyes or to one’s mind as influenced by one’s feelings or sentiments.
Hallucination implies the perception of visual images or, less often, of other sensory impressions (as sounds or odors) that have no reality but are the product of disordered sensory organs, nerves, or mind or are associated with particular disorders (as delirium tremens or intense fever).
Mirage is comparable with the preceding terms only in its extended sense in which it usually applies to a vision, dream, hope, or aim which one takes as a guide, not realizing that it is merely an illusion.