Web API (Application Programming Interface):

1. Exposes Appian's data and services to external systems. This means an external system initiates the call to Appian.
2. Allows other applications to interact with Appian, for example, to create, read, update, or delete records within Appian, or to trigger Appian processes.

Example:

1. Scenario: A custom public website has a "Contact Us" form, and submissions need to initiate a case management process in Appian.
2. Solution: Create a POST Web API in Appian.
3. When a user submits the form on the website, the website sends a POST request containing the form data to the Appian Web API endpoint. The Web API then starts a specific Appian process model to handle the new case.

Integration Object:

1. Enables Appian to call and interact with external systems. This means Appian initiates the call to an external system.
2. Allows Appian applications to retrieve data from external systems, send data to external systems, or trigger actions in external systems.

Example:

1. Scenario: An Appian user interface needs to display the current weather forecast based on a location the user enters.
2. Solution: Create an Integration object that calls an external weather service API (e.g., OpenWeatherMap). This integration is linked to a Connected System object that holds the API key for the weather service.
3. When the user enters a city in the Appian interface, the integration is called with the city name as a parameter. Appian sends a request out to the weather service API, receives the JSON response, and displays the temperature in the interface.