How many types of API are there?

An application programming interface (API) establishes an online connection between a data provider and an end-user. For financial markets, APIs interface trading algorithms or models and an exchange's and/or broker's platform. An API is essential to implementing an automated trading strategy.

  There are four principal types of API commonly used in web-based applications: public, partner, private and composite.
Public APIs: A public API is open and available for use by any outside developer or business. Public APIs typically involve moderate authentication and authorization. 
Partner APIs: A partner API, only available to specifically selected and authorized outside developers or API consumers, is a means to facilitate business-to-business activities. Partners have clear rights and licenses to access such APIs.
Internal APIs: An internal (or private) API is intended only for use within the enterprise to connect systems and data within the business. Internal APIs traditionally present weak security and authentication -- or none at all 
Composite APIs: Composite APIs generally combine two or more APIs to craft a sequence of related or interdependent operations. Composite APIs can be beneficial to address complex or tightly-related API behaviors, and can sometimes improve speed and performance over individual APIs.