To explain polarisation, my book gives an example of a transverse wave in a string, and explains as:
Since each point on the string moves on a straight line, the wave is also referred to as a linearly polarised wave. Further, the string always remains confined to the x-y plane and therefore it is also referred to as a plane polarised wave
The image given is somewhat like this: 
The definitions for both these terms are different, so it seems to me that they are not same. But I wasn't able to find an example which illustrates the difference between these two.
I found this Quora question, but the answers don't seem convincing.
So what exactly is the difference between a linearly polarised wave and a plane-polarised wave? Because according to me, a linearly polarised wave will oscillate in only one plane.
Best Answer
Linearly polarized wave is same as plane polarized wave. Why we call it linearly polarized ? Because oscillation taking place along a line. Why we call it plane polarized ? Since oscillation taking place along one axis & the wave is forward in motion along another axis. Two axes are used , so called plane.