LCD stands for "Liquid Crystal Display". They aren't the same thing at all- in fact, WLED screens also have
LCD displays. LCD's are what refracts the light in them. the difference is in the backlighting. Standard LCD screens have a CCFL on top and on bottom of the screen (anyone who has disassembled an LCD knows this), and these light the entire screen, which means there will be uneven light conditions at different parts of the screen, and a true black is impossible, because the CCFL's can't cause just certain parts of the screen to go completely dark. This is where WLED comes in- it has LEDs evenly distributed throughout the back of the screen, which as you said, turn off individually to achieve true black.
What you got wrong there is that LCDs are not a form of backlighting and that WLEDs use an evenly distributed array, whereas standard LCDs use an imbalanced twin-large-light array that cannot achieve the same depth of lighting that WLED can. So to answer, yes, WLED screens are better.
Here's a good read on the slight details you missed that led you to that conclusion: