How equals() method works

String class has overridden the equals() method . Please follow the String#equals() documentation.

a.equals(b) has returned true, meaning the condition a==b is satisfied

This is the default implementation of equals() in the Object class , String class has overridden the default implementation. It returns true if and only if the argument is not null and is a String object that represents the same sequence of characters as this object.

Aren't hashCode and address one and same?

Not necessarily , for further reading on hashCode().

No, Hashcode and address aren't the same.

Because a==b is not comparing hashcodes.

Yes, something else is compared when we say a==b.

(that's not addresses either, really, but it's close enough).

Also, just because "equal objects have equal hashcodes" does not mean "equal hashcodes means equal objects".

The == operator in Java compares object references to see if they refer to the same object. Because your variables a and b refer to different objects, they are not equal according to ==.

And the hashCode method doesn't return the address in String, because that class has overridden hashCode.

Additionally, the equals method has been implemented in String to compare the contents of the strings; that's why a.equals(b) returns true here.