I have heard about these different types of screens on DIY websites and in consumer electronics. What are the differences in these types of screens and what are their advantages and disadvantages?
LCD: liquid crystal display. Works by adjusting the amount of light blocked. Usually has a backlight but might not (clocks, calculators, Nintendo Gameboy). The green-black ones can be very cheap and are a mature technology. Response time can be slow.
TFT: is a type of LCD with a thin film transistor attached to each pixel. All computer LCD screens are TFT since early 2000s; older ones had slower response times and poorer colour. Cost is now very good; power consumption is fairly good but dominated by the backlight. Has to be manufactured out of glass.
LED: light emitting diode. As the name suggests, emits light rather than blocking it like LCD. Used for red/green/blue/white indicator lights everywhere. Some manufacturers advertise "LED" displays that are TFT screens with a white LED backlight, which is just confusing. Ones that are real LED screens are usually OLED.
OLED: organic LED (rather than silicon or germanium based like regular LEDs). Comparatively recent technology, so cost still quite variable and not available in really large sizes. In theory can be printed on plastic, resulting in lighter flexible displays with good brightness, good power consumption and good response time.
Best power consumption of all of these is a monochrome infrequently changing LCD display with no backlight.