Double hits

13.3

[It shall be a fault] if in play, the shuttle:

13.3.7

is caught and held on the racket and then slung during the execution of a stroke;

13.3.8

is hit twice in succession by the same player. However, a shuttle hitting the head and the stringed area of the racket in one stroke shall not be a fault;

13.3.9

is hit by a player and the player’s partner successively;

With a little practice, it’s possible to catch the shuttle with your racket, using a scooping motion. For obvious reasons, you’re not allowed to do this during a rally.

Similarly, you may not hit the shuttle twice, on your own or with a partner — for example, first hitting it up above net height, and then smashing it down!

Note that a bad contact is not a fault. Many players, especially older ones, call no shot when they have made a bad contact — either hitting just the frame, or hitting both the frame and the strings. This is not a fault, and the rally should continue.

The above is copied from the Badminton Bible wesbite regards double hits and I think explains it quite well.

In the case of the player who called his own 'fault' it would depend whether the shuttle struck the frame then strings, or slid from the frame to the strings.