What is the difference between GUI and API?

GUI - Graphical User Interface

API - Application Programming Interface

In short, a GUI is the user-facing side of a program, the part that a user (typically, human) interacts with, and controls the program with. Common elements of such interfaces are buttons, text fields, check boxes, etc.

An API is generally used by a program (rather than a human) to interact with or control another program. One example is the eBay API, which allows a program to upload items for sale on ebay.com, as opposed to manually uploading the item for sale using eBay's GUI.