What is the difference betwen “ESP8266Wifi.h” and “WiFiEsp.h” libraries?
It's quite simple:


ESP8266WiFi.h - Runs on the ESP8266 to control the WiFi.
WiFiEsp.h - Runs on an Arduino to communicate with an ESP8266 module with AT commands
WiFi.h - Runs on an Arduino to work with the Arduino WiFi shield.


So the one you want, which is part of the ESP8266 core, is ESP8266WiFi.h.