The difference is the way the TVs are lighted. They both use LCD displays. LCD TVs have CFL (florescent) backlighting, and LED TVs have actual LEDs lighting them.
As far as one being better, LED TVs use less energy. They are also much thinner because they can be lit from the sides. For more technical information, I found this link may be useful to you: http://www.lcdtvbuyingguide.com/hdtv/led-vs-lcd.html
There are also TV's that use OLEDs. OLEDs are LED arrays manufactured directly on a thin film. This method allows the manufacturer to create a display screen with very high resolution that does not need a backlight. Thus the screen, when placed in a TV can be very thin.
Sony has commercialized a TV based on this. It's small and pricey.
There was some hope that this technology would improve quickly and costs would drop. While there are cell phones, music players and other small devices that use them, OLEDs have not taken off in large TVs.
My old MP3 player had an OLED screen, thing was that they still made it quite chunky so it was small...
Also, the OLED can be flexible... Somehow. All the colour change artists you see also have clothing embedded with OLEDs; hence they can change so quickly.
I have seen one additional benefit being exploited from some LED backlight TV's although not one that would win me over. Since the backlight is not just one LED bulb but a number of them they play a trick to increase the contrast ratio (make the black blacker) They do this by turning off the backlights in the corresponding dark areas of the screen. It does make a difference you can see, although not a huge one to me.