Both of these styles result in images that are created to look real, but don’t really exist. Therefore, there will be some occasions when you can not tell the difference, but use these guides and most of the time you will be able to figure it out.
Surreal art is based on dreams and often irrational. It frequently includes things that look out of place…melting clocks, floating apples, a giant glass in the middle of a field… The work itself does not provide a framework for understanding the bizarre things within it.
Fantasy art is imaginary, but typically tied to a story…superheroes, orcs and hobbits, castles, fairies… In a good fantasy work, everything makes sense within the context that it provides.
Can something be both? Yes, but for the purposes of learning these styles, we are going to try to classify them as one or the other.