Why are the equations w - x x = w and w x - x = w called identities?

They are called identities because:

w-x = 0

w = x (carry x to the other side) is the same as x = w

in the other case:

wx-x = w / divide by w on both side

x - x = 0

x = x (carry x to the other side)

In both cases the equations are the same.