The LEDs are really an advancement of the LCD. The reason a LED is thinner is the back lights are around the side, instead of behind. Both are good. I have been looking at a TCL LCD & LED and the pics on both are fabulous.
Basically the LEDs are for backlighting only. The replace flourescent backlightng which was the norm for LCD's. The do have real LED tv's coming out, OLED, but they're vry expensive right now and are only in smaller tv's.
The back light is LED, and all LED TV's are LCD, but not all LCD's are LED. There is florescent back lit TV's, and that technology is on the way out if not gone. There are 2 types of LED's at this time, edge lit just about all and some that are called full array, rare, more led's and more money. I have Vizio edge lit LED-LCD's from the last 3 generations and very happy with them.