Ethernet shield or Wifi sheild - Arduino? To control some LEDs through internet using Arduino UNO, which type of connection  is better ? Ethernet or Wifi? (Later, I may connect some relays instead of LEDs, and control (turn on and off) some devices using this setup). 
The only difference I know is the wired and wireless connectivity. 
Is there any other difference?
If you are beginner with Arduino its better to start with Ethernet Shield. Its much more easy to connect with Arduino.

WiFi Module - ESP8266 required some more knowledge, that you will learn in future.

The bought products are cheap, so you can start with Ethernet and after that to switch to ESP.