A playwright is someone who writes plays for the theatre — the script that actors perform on a stage. Shakespeare is a playwright; so is a living writer whose new play is on in London or Taipei. The word is neutral and standard: newspapers, school books, and theatre programmes all use it. It is not the same as a screenwriter (films and TV) or a poet, though one person can be more than one of these. The second half looks like write, and students often spell it that way, but it is wright, an old word for a maker or craftsman. A playwright ‘builds’ a play, in that old sense. You can say female playwright; playwright itself is not gendered.