Below I have compiled a different comedy forms with descriptions.
Low Comedy requires little skill in the scripting .Often a visual or highly physical work.
Parody is similar to satire as it is a work that deliberately imitates another work for comic effect, sometimes delivering a message. See YouTube for many examples of parodies of contemporary people and world events.
Stand-up is a type of comedy normally involving one person performing a comic routine before a live audience.
Black Comedy / Black Humour is humour that makes fun of serious subject matter such as death and religion. Offensive to some, hilarious to others. Requires intelligent scripting.
Travesty is a work that misrepresents serious subject matter via parody.
Romantic Comedy is comedy involving love and romance. Many of Shakespeare’s comedies are romantic comedies.
Musical Comedy Musical theatre is mostly (not always) comic in some way, hence lighthearted and appealing to the masses.
Sentimental Comedy Not really a comedy at all, but plays that involve the main character overcoming a series of moral challenges.