equals() method v/s == operator

It is important to understand that the equals( ) method and the == operator perform two different operations.
For String class

equals()	Compares the characters inside a String object, i.e.) it compares the contents of the String object.
== operator	Compares two references to see whether they refer to the same object in the memory

Example 1:

package com.ibytecode.strings.methods;
public class EqualsAndEqualToOperator {
	public static void main(String[] args) {
		String s1 = "abc";
		String s2 = "abc";
		if(s1.equals(s2))
			System.out.println("s1.equals(s2) is True");
		if(s1 == s2)
			System.out.println("s1 == s2 is True");
	}
}

s1.equals(s2) is True
s1 == s2 is True

As already explained in string literal pool JVM creates a new String object in constant pool and makes s1 refer to it. Now for creating s2, it checks the String constant pool and since the string already exists a reference to the pooled instance is returned to s2.
Hence the above code creates,

1. Two references, s1 and s2
2. One String object “abc”

Example 2:

package com.ibytecode.strings.methods;
public class EqualsAndEqualToOperator {
	public static void main(String[] args) {
		String s3 = "abc";
		String s4 = new String("abc");
		if(s3.equals(s4))
			System.out.println("s3.equals(s4) is True");
		if(s3 == s4)
			System.out.println("s3 == s4 is True");
		else
			System.out.println("s3 == s4 is False");
	}
}

s3.equals(s4) is True
s3 == s4 is False

The above code creates,

1. Two references, s3 and s4
2. Two String objects “abc” in literal pool and one string object “abc” on heap

Refer string literal pool tutorial for more datails

Example 3:

package com.ibytecode.strings.methods;
public class EqualsAndEqualToOperator {
	public static void main(String[] args) {
		String s5 = new String("abc");
		String s6 = new String("abc");
		if(s5.equals(s6))
			System.out.println("s5.equals(s6) is True");
		if(s5 == s6)
			System.out.println("s5 == s6 is True");
		else
			System.out.println("s5 == s6 is False");
	}
}

s5.equals(s6) is True
s5 == s6 is False

Example 4:

package com.ibytecode.strings.methods;
public class EqualsAndEqualToOperator {
	public static void main(String[] args) {
		String s7 = new String("abc");
		String s8 = new String(s7);
		if(s7.equals(s8))
			System.out.println("s7.equals(s8) is True");
		if(s7 == s8)
			System.out.println("s7 == s8 is True");
		else
			System.out.println("s7 == s8 is False");
	}
}

s7.equals(s8) is True
s7 == s8 is False