Noise is a term for distortions in a signal; there are many. many, different natural causes of noise, e.g. so-called 'thermal' noise, caused by the random motion of electrons in the conductors of a circuit, noise from natural phenomena such as lightning, solar radiation, etc.
Interference is the term often used for the subset of noise which is not natural, but comes from other electrical systems; e.g. crosstalk, or radio and television transmissions, noise from industrial sources such a car ignitions, etc.
Noise can occasionally be useful, e.g. as input to a random number generator.