It stands for Low-Voltage Differential Signaling (LVDS). It is a type of serial connection to data source. A complete definition can be found here: https://en.m.wikipedia.org/wiki/Low-voltage_differential_signaling
Almost all older (pre-2013) laptops use LVDS display cables. Common to laptops are 30-pin and 40-pin cables.
It stands for Embedded Display Port (EDP). It is used in newer laptops which allows for the use of higher resolution display screens. These cables allow for higher refresh rates, color depths and higher resolutions. It also uses less power than LVDS cables which translates into slightly longer battery life.
Unfortunately, you cannot switch or upgrade your cable from LVDS to EDP technology in a laptop. You must use the exact same cable that was used to match the current display in your laptop to the motherboard. While it may be possible to upgrade your cable AND display most motherboards would need to be changed as well to support this change.
LCD displays use cold cathode fluorescent lamps (CCFL) while LED displays use are backlit using light-emitting diodes (LEDs) to illuminate the display. The cable used in your laptop would be properly paired with the display type used.
LCD and LED cables are both commonly referred to as LCD cables when used in laptops.