A playwright, also known as a dramatist, is a person who writes dramatic literature or drama. These works are usually written to be performed in front of a live audience by actors. They may also be closet dramas or literary works written using dramatic forms but not meant for performance.
The term is not a variant spelling of "playwrite", but something quite distinct: the word wright is an archaic English term for a craftsman or builder (as in a wheelwright or cartwright). Hence the prefix and the suffix combine to indicate someone who has wrought words, themes, and other elements into a dramatic form, someone who crafts plays. The homophone with write is in this case entirely coincidental.
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