The Cloud Foundry API is a RESTful interface exposed by the Cloud Controller. You may hear this API referred to as CAPI, an abbreviation for the Cloud Controller API. The Cloud Controller API is also part of the common core, meaning it is standard across the different vendor distributions.
When you set an API endpoint, you are selecting a deployment of Cloud Foundry to use. You may hear some vendors refer to deployments as “foundations” or “instances”, but they are essentially one and the same. They are a running Cloud Foundry deployment.