The connection standard used for MOST but not all large flat-panel displays (inside notebook computers and flat screen monitors) is called FPD-Link (also called LVDS colloquially. FPD-Link is based on LVDS, but not every LVDS interface is FPD-Link or even a display interface at all). Some other designs are known to use the "embedded display port" interface.
This is an interface that is not meant to be interacted with by consumers, but engineers, knowledgeable repair personnel, and people (professional or amateur) with equivalent knowledge.
FPDLink does not have entirely standardized physical connectors, and in the worst case the connectors on a certain display and a certain computer would physically mate but be differently wired, resulting in non-function or even equipment damage.
Before even trying to "transplant" such panels, check:
if available, the datasheets for both display panels. Compare power requirements (a panel might initially work but overload and stress the power supply!), pinouts.
Backlighting components might not be considered part of the display assembly, and thus not be in the panel datasheet, even if they are glued onto it.
If backlighting parts are seperately wired, are they compatible? The fact that connectors physically mate is not sufficient. Especially, do not even try to mix and match backlights and backlight power supplies (in case the backlight power supply is external to the panel). There might be a datasheet available on the web on the backlight power supply modules, you would need to compare input power requirements, pinouts...
if no datasheet is available, compare the wiring in both systems - do twisted wire pairs (or thicker pairs of traces on a printed cable) go to the same pins?
Be aware that electronics modules that are not meant to be user-serviceable tend to REALLY dislike (read: you might get away with them, but you might also permanently wreck the component!) some behaviours easily incurred when experimenting around:
- Applying power to multiple power inputs (eg 5 and 12V) at different times
- Applying power with signal inputs physically disconnected (different thing from "connected to a signal source that is powered off!")
- Having ANY input pin (unless the datasheet says it is OK), even if the function assigned to it is not needed, physically not connected while running.
- Applying ANYTHING to more than one pin while the circuit ground is physically disconnected
- Applying signals while the receiver is unpowered
- Applying power while signals are already being applied
Explanation for many of these: A lot of circuit designs rely on signal voltages being above the voltage on circuit ground (being disconnected does not count as being at 0 volts!) and below the voltage on a given power input at any given time, and will crash horribly if these assumptions are violated - and most of the scenarios described do exactly that. The last scenario I described is well known to be fatal to these old-school, one or two line alphanumeric LCDs (HD44780 type. Different from a notebook display, but... ) often found on industrial equipment - they tend to go up in smoke if you do that).
Also, be aware that old-style (pre-LED) backlight systems are not toys - there is voltage high enough to both shock you and damage other parts of the equipment if accidentally shorted into them. Also, the backlight tubes in these combine the features of being easily broken and being toxic when broken.