no, the WiFi library is only a thin layer over the SDK handling WiFi and LWIP handling TCP/IP.
I try to conclude what you explain, please correct me if I'm wrong. So, the Wi-Fi library is handling simple things such as allow the programmer to set the Wi-Fi password, Wi-Fi SSID, enabling WEP encryption, etc.? Basically allowing programmer to do the setting that they want? And after the programmer done all those setting, the library in Arduino will interact with the library from Espressif, then the library from the Espressif will do the complicated stuff of giving instruction to the ESP to perform the Wi-Fi function?
And from this link that you have provided: https://www.espressif.com/sites/default/files/documentation/2c-esp8266_non_os_sdk_api_reference_en.pdf, I read about this:
The non-OS SDK provides a set of application programming interfaces (APIs) for core ESP8266 functionalities such as data reception/transmission over Wi-Fi, TCP/IP stack functions, hardware interface functions and basic system management functions.
Is the API here same as the library from Espressif that you mentioned previously?