Why Fluent Interface is called Fluent API

Why Fluent API is called "API" ? Fluent API is a way to create fluent Domain Specific Language, whereas API is "Appication Programming Interface". API is:

"A set of functions and procedures that allow the creation of applications which access the features or data of an operating system, application, or other service."

"An application programming interface (API) is a set of protocols, routines, functions and/or commands that programmers use to develop software or facilitate interaction between distinct systems."

So how this two definitions containing words "Distinct system", "Access features" relate to Fluent Interface pattern? Even Martin Fowler sometimes names it API: https://martinfowler.com/bliki/FluentInterface.html

Please, tell me, what's wrong with my or other's idea about API? Maybe we should stop calling screwdrivers all long metal rods with handles?