Casting to string only works when the object actually is a string:
Object reallyAString = "foo";
String str = (String) reallyAString; // works.
It won’t work when the object is something else:
Object notAString = new Integer(42);
String str = (String) notAString; // will throw a ClassCastException
String.valueOf() however will try to convert whatever you pass into it to a String. It handles both primitives (42) and objects (new Integer(42), using that object’s toString()):
String str;
str = String.valueOf(new Integer(42)); // str will hold "42"
str = String.valueOf("foo"); // str will hold "foo"
Object nullValue = null;
str = String.valueOf(nullValue); // str will hold "null"
Note especially the last example: passing null to String.valueOf() will return the string "null".