LED LCD TVs/Monitors have LED backlights, but still use LCD panels. The name "LED TV" generally means it's actually LED LCD. It's a marketing gimmick, meant to confuse people more than anything.
OLED TV's/Monitors are the ones with actual LEDs for each pixel. Premium smartphones also use OLED screens.
The 16x2 LCD you referred to is a 16x2 CHARACTER LCD. It's not really meant to be pixel-addressable.
LCD screens have embedded controllers in them that control the panel itself. When you want to display something on that panel, you communicate with that embedded controller. The way you interface with the controller depends on the controller/panel type. Typically, with the smaller screens, it's via something like I2C or SPI. With full-blown TV/Monitor panels, it's usually via multiple LVDS channels.