Format and Structure
The standards for screenwriting, such as format and overall story structure, do not change often across genres. The first act still introduces the characters, presents the problem, and the main character’s acceptance of the challenge. The difference here is going to be at what speed these things come, though not in the order. For example, dramas tend to have longer openers as they need to present a more solid situation, characters, and perhaps a more serious challenge. Comedies set up themselves and their perspective relatively quickly as they are more than just a storytelling vessel, and the same often comes through horror films. Genres that have a more specified audience tend to allow themselves to keep their overall point of view, and general story facts, present from the first couple minutes.
The type of genres that are really going to change the general format for screenwriting are going to be those that challenge the norms of narrative filmmaking in general. For example, a mockumentary will tend to break free from the regular screenwriting genres and may even just use an outline. This is going to be incredibly true for films that use a great deal of improvisation, such as Mumblecore or Dogma 95. These may have alternative screenwriting options, and since they are genre only in their specific approach and filmmaking movement they are not going to work the same as basic genres like romance or action.
Many adventure and action films will have screenplays that hold fewer dialogue centered scenes, and a lot of less descriptive prose passages. This is because the action that you end up seeing on screen cannot be determined specifically in the script and will be done so by the director, stunt people, and action coordinators when they are actually working on the film. Instead, you may end up seeing very simple lines that then translate into several minute long action sequences. The exact nature of this is going to depend on the film, but this may be the case for special effects as well unless they are centered on a character and essential for understanding the story and mood when you are actually reading the script.