Web Services is a standard means of operating b/w diff. software applications, running on variety of platforms. Ex. XML-RPC uses XML for encoding/decoding the remote procedure call (RPC) and the respective parameter(s), JSON-RPC, SOAP,
APIs are basically a set od rules that enables data transformation b/w diffrent software, Kinda like a waiter b/w the web app, and the backend.
WSDL stands for web service description language, XML based file exposed by web services that informs client of the provided services, methods.