The O. Henry Award is given for especially good short stories. The prize is given each year. The award is named after the American short story author, O. Henry.
The PEN/O. Henry Prize Stories is a book that is published each year with that year's twenty best stories from magazines in U.S. and Canadian, written in English.
The award itself is called The O. Henry Award, not the O. Henry Prize, though until recently there were first, second and third prize winners.