In very simple cases, like 2!=3, the answer is immediately True, but usually != is meant for further processing, like equation solving. x-1!=0 is solved as x!=1. By itself, x-1!=0 is left as it is.
The test for literal inequality is =!=. It has a different purpose. x-1=!=0 gives True, because the two sides are not the same expression.
Check out the documentation about Unequal and UnsameQ.
