A wish is a hope or desire for something. In fiction, wishes can be used as plot devices. In folklore, opportunities for "making a wish" or for wishes to "come true" or "be granted" are themes that are sometimes used.
A fairy offering wishes, illustration by John Bauer to Alfred Smedberg's The seven wishes
Wishes written on red ribbons and tied to a tree in Beihai, Guangxi, China
Hope is an optimistic state of mind that is based on an expectation of positive outcomes with respect to events and circumstances in one's life or the world at large.
As a verb, its definitions include: "expect with confidence" and "to cherish a desire with anticipation".
A Syrian refugee girl with a hopeful expression
Hope, which lay at the bottom of the box, remained. Allegorical painting by George Frederic Watts, 1886
A rose expressing hope, at Auschwitz concentration camp
Engraving of Pandora trying to close the box that she had opened out of curiosity. At left, the evils of the world taunt her as they escape. The engraving is based on a painting by F. S. Church.