what does Drupal API mean?
It's a generic term to encapsulate all the programming interfaces Drupal provides. Any further meaning would have to be inferred from the context of how it was used (FWIW, I've never heard "Drupal API" to refer to the documentation site api.drupal.org). 

When specifying a particular component of the Drupal API, you'll often see it labeled with its functionality (e.g. Drupal Routing API, Drupal Batch API, etc.) to clarify what part of Drupal's API is being discussed.