The official Harry Potter and the Cursed Child script will be released in the USA on July 25, 2017.
At the moment only the special rehearsal edition can be purchased.
The difference between the two is:
This revised paperback edition updates the “special rehearsal edition” with the conclusive and final dialogue from the play, which has subtly changed since its rehearsals, as well as a conversation piece between director John Tiffany and writer Jack Thorne, who share stories and insights about reading playscripts. This edition also includes useful background information including the Potter family tree and a timeline of events from the wizarding world prior to the beginning of “Harry Potter and the Cursed Child”.