The basic difference between them is memory allocation.
First option i.e
String s1 = "hello";
When you use this s1 is called as a string literal and memory for s1 is allocated at compile time.
But in 2nd case
String s2 = new String("hello");
In this case s2 is called as an object of String representing hello
When you tries to create two string literal using the first case, only one memory is referenced by those two literals. I mean String literals are working with a concept of string pool. when you create a 2nd string literal with same content, instead of allocating a new space compiler will return the same reference. Hence you will get true when you compare those two literals using == operator.
But in the 2nd case each time JVM will create a new object for each. and you have to compare their contents using equals() method but not with == operator.
If you want to create a new string object using 2nd case and also you don't want a new object, then you can use intern() method to get the same object.
String s = "hello";
String s1 = new String("hello").intern();
System.out.println(s == s1);
In this case instead of creating a new object, JVM will return the same reference s. So the output will be true