4x4 parity occurs on the last layer of a 4x4, where you get a case that is impossible to get on a 3x3 so you need a specific algorithm to solve it.  PLL parity specifically occurs because two adjacent edge pieces are swapped diagonally with 2 other adjacent edge pieces.  Generally you can't recognize it until you are at the PLL stage of solving.

PLL Parity case 1:

This swaps the 2 edges opposite each other

r2, U2, r2, Uw2, r2, u2 4x4 PLL Parity  Algorithm

 

 

PLL Parity case 2:

This swaps the 2 edges adjacent each other

(R' U R U' ) r2, U2, r2, Uw2, r2, u2, (U R' U' R ) 

 

 

 

Rw BOTH Right Layers
r INNER Right Layer
Uw BOTH Top Layers
u INNER Top Layer
X Turn the cube clockwise around the X-Axis
X'  Turn the cube anti-clockwise around the X-axis