There is no explicit difference between a Wi-Fi repeater and range extender; both devices perform the same function of extending the range of an already existing wireless Internet network. Manufacturers often use the terms repeater and extender interchangeably to describe their products and functionality.
A Wi-Fi repeater or range extender functions as if it has two Internet routers in one device. One Internet router inside of the repeater/extender connects to the already existing Wi-Fi network. The second router inside of the repeater/extender then broadcasts that Wi-Fi network beyond the range of the original router to extend the scope of the network. Since the Wi-Fi network is being shared between two devices that share the same bandwidth, it is possible for the user to experience a loss of overall Internet speed. Most repeater/extenders offer the same network protection as traditional routers, those being WEP, WPA and WPA2.
Since the Wi-Fi extender/repeater is simply boosting the range of the original wireless network, put the extender in a location where it can receive a strong signal from the original wireless router. Putting the extender/repeater in a location where it cannot optimally receive data from the original router slows down the entire network and results in poor performance.