Harlowe, SugerCube, and Snowman are Story Formats.
There are two main components to 'Twine': the Twine application(s) and the Story Formats.
2. A Story Format is a mini web-application. it uses the information contained within the embedded Passages to generate the web-page shown to the Reader. It is responsible for defining the custom macro language used by the Author, the core functionallity of the story, as well as it's default visual layout & styling.
This is why the choice of which Story Format you use to write your story is important.
Harlowe is the simplest story format, it has been designed for beginners with limited (or no) programming experience. It can be simple to learn however that simplicity comes at a cost, it has performance issues when dealing with certain types of information and it can be difficult to extend the story format's core functionallity.
Snowman is the hardest story format to use, it has been designed with web-developers in mind. It includes very little core functionallity, the Author is expected to write all require functionallity themselves.