I think it's wierd that i have to say: if x and y is 0 then no division.. 
On the contrary, if you want no division to occur when either of x or y is 0, you must not divide
if x or y is 0.
You use && when you want to evaluate whether "condition a is true and condition b is true". You use  when you want to evaluate whether "condition a is true or condition b is true."
That's why for me it's much more logical to use  (or), because then it doesn't devides if just 1 of them is 0.. 
You used or with inequality which, not surprisingly, leads to different results than using or with equality.
The original code you supplied (well, at least the second snippet) looks like:
1 2 3 4

if(y != 0  x != 0)
// do division
else
// don't do division

In English: If y is not 0
or if x is not 0, do division. The problem there of course is that x can be not 0 while y is 0, and the condition evaluates to true, because that's what we asked for.
Consider what the if statements look like for particular values of x and y when the expressions are replaced with the true or false value they evaluate to:
x = 0, y = 0
if ( y!=0  x!=0 ) > if ( false  false ) > false
x=1, y=0
if ( y!=0  x!=0 ) > if ( false  true ) > true
x=0, y=1
if ( y!=0  x!=0 ) > if ( true  false ) > true
x=1, y=1
if ( y!=0  x!=0 ) > if ( true  true ) > true 