Key difference: Dreams can be defined as a series of successive visions, images, and feelings experienced by a person during his/her sleep. Fantasy is imagining improbable things, which have no basis in reality. 

Dreams are the soul of a good night’s sleep. If a person is dreaming, then more often than not, he/she is experiencing a very sound sleep at that moment. Dreams revitalize our brain by de-cluttering it. They also make our mind available for fresh absorption of facts and data. Over the years gone by, many professors, scientists, psychologists, et al. have tried deconstructing the true nature of dreams. However, there have been no standout breakthroughs as such in this field. Despite this fact, the phenomenon of dreaming still captures the imagination of these professionals, and never ceases to amaze one and all. See Dream Vs. Nightmare 

Fantasy often helps people experience the impossible in a subtle manner. Fantasy means the act of imaging things that are a departure from stark and existential reality. Fantasies could be anything that is consciously or subconsciously deep-rooted in a person’s mind. They can range from being simple to being brutally complex or brilliantly inspiring. Fantasies often transcend the scientific barriers of sense and rationality, by involving themes like magic and supernaturalism. For instance, the Harry Potter series by the acclaimed author, J.K. Rowling, is a notable example of fantasy. 
See: Dream Vs. Reality

Comparison between a Dream and Fantasy:

See: Deja Vu Vs. Dreams  

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