If we compile them into two methods in java

private StringBuffer sb = new StringBuffer("Welcome");

public String testToString() {
  return sb.toString();
}

public String testAppend() {
  return sb + "";
}

and then use javap -v, we get

public java.lang.String testToString();
  descriptor: ()Ljava/lang/String;
  flags: ACC_PUBLIC
  Code:
    stack=1, locals=1, args_size=1
       0: aload_0       
       1: getfield      #19                 // Field sb:Ljava/lang/StringBuffer;
       4: invokevirtual #27                 // Method java/lang/StringBuffer.toString:()Ljava/lang/String;
       7: areturn       
    LineNumberTable:
      line 10: 0
    LocalVariableTable:
      Start  Length  Slot  Name   Signature
          0       8     0  this   Lcom/stackoverflow/Question;

public java.lang.String testAppend();
  descriptor: ()Ljava/lang/String;
  flags: ACC_PUBLIC
  Code:
    stack=2, locals=1, args_size=1
       0: new           #31                 // class java/lang/StringBuilder
       3: dup           
       4: invokespecial #33                 // Method java/lang/StringBuilder."<init>":()V
       7: aload_0       
       8: getfield      #19                 // Field sb:Ljava/lang/StringBuffer;
      11: invokevirtual #34                 // Method java/lang/StringBuilder.append:(Ljava/lang/Object;)Ljava/lang/StringBuilder;
      14: invokevirtual #38                 // Method java/lang/StringBuilder.toString:()Ljava/lang/String;
      17: areturn       
    LineNumberTable:
      line 14: 0
    LocalVariableTable:
      Start  Length  Slot  Name   Signature
          0      18     0  this   Lcom/stackoverflow/Question;

So appending appears to be slightly less efficient as it uses an extra bit of stack and contains more instructions.

String is final and immutable too.

Hence, this class cannot be extended or inherited by any other class. So, there is no IS-A Relationship between these two classes. String can never be converted or referenced to any other Class except java.lang.Object directly.

But StringBuffer provides a Constructor through which you can convert a String into a StringBuffer Object.

public java.lang.StringBuffer(java.lang.String); //pass string as an argument. StringBuffer object will you get.

In your case, try this code:

addFilter(new StringBuffer(keyword)).toString();

sb.toString();//what is happening here?

You are converting the StringBuilder object to String which is good but you are not storing the return value to a String type and using it later in your equals call. You should do it the following way:

String reversedString = sb.toString();
if(s.equals(reversedString )){

Or simply

if(s.equals(sb.toString())){

Right now you are comparing s with sb using the equals method of String class. This method returns false if the object passed in as an argument is not an instance of String class. Since StringBuilder object sb is not an instance of String, the equals method returns false.