That's because you're comparing the whole String, and apparently you seem to be thinking it checks every substring split at the space which honestly doesn't work that way (it would be unintuitive too).

So,

String one= "ROLEAWARDS ROLEMOVIES ROLENOMINATIONS"; 
String two = "ROLENOMINATIONS ROLEAWARDS ROLEMOVIES";

String[] oneSplit = one.split(" ");
String[] twoSplit = two.split(" ");
boolean contains = false;
for(int i = 0; i < oneSplit.length; i++)
{
    for(int j = 0; j < twoSplit.length; j++)
    {
        if(oneSplit[i].contains(twoSplit[j])
        {
            contains = true;
            break;
        }
    }
}
if(contains)
{
    System.out.println("Contains");
}
else
{
    System.out.println("Doesn't Contain");
}