No, a side effect is not necessarily observable behaviour. Modifying a non-volatile object, for example, is a side effect, but not observable. The difference matters because the side effects may be rearranged or removed altogether by the compiler, so long as the observable behaviour remains the same.
int main()
{
int a;
a = 30;
a += 2;
return 0;
}
Most compilers will, if requested, remove a
completely. That's permitted. The assignments and addition aren't observable.
All observable behaviour must necessarily be a side effect though.