Yeah I think we're saying kind of the same thing but in different ways.
Active matrix LCD displays don't emit light and therefore require some form of back lighting usually CCFL, HCFL or LED.
The positioning of the lighting sources is open to different alternatives but the ultimate purpose is to provide as even as possible a light behind the LCD display (otherwise you couldn't properly see the image being displayed).
RGB dynamic LEDs are placed behind the display and allow for localised dimming which can enhance black levels.
Edge LEDs diffuse the light behind the screen with a special panel and as you say allow for slimmer designs.
In general LEDs are superior to CCFL as they have a wider colour gamut, higher dynamic contrast and use less power (typically 20-30% less).
OLED is one of a number of self illuminating technologies including OEL and more recently AMOLED which is now being increasingly used in digital cameras and mobile phones.
As all these technologies emit their own light, additional back lighting isn't normally required.