Noise can be Differential or Common!
Imagine a perfect noiseless signal transmitted down two wires and you looked at what was received at the other end. Along the way, noise impregnates the two wires. What you might see at the receiving end is a noise voltage that exists between the two wires (differential). You will likely also see a noise voltage that affects both wires exactly the same with respect to ground (common mode). 

The differential noise is effectively added to your signal and unfortunately, cannot be got rid of without special techniques. The common mode noise (both wires affected the same) can be eradicated by a decent differential amplifier i.e. it only amplifies the differential signal and is unaffected by common mode signals or noises.

Here's an example of a sudden spike of common mode noise affecting a differentially transmitted signal: -



The same noise signal affects both wires but, because a differential amplifier is used to receive the signal, that noise is cancelled out in the receiver.

However, if that noise affected one wire more than the other it would produce a differential noise and adds to the signal and cannot be eradicated easily. There are things that can be done but, I feel, it's beyond the scope of the question to go into these.

To avoid common-mode noises (the main source in a lot of installations) becoming differential noise, the following safeguards are observed: -


Differential signals are transmitted
Driving impedances (sending end) are matched
Differential amplifiers are used at the receiver
Receiving impedances to ground are matched
Decent twisted pair is used preferably with a screen


In addition to this, the cable at the receiving end may have a terminator to match impedances and prevent relections.