Caliber confusion is such fun.
When MOST people say "9mm", they mean 9x19, also known as 9mm Luger, also known as 9mm Parabellum.
But, 9mm is just the diameter of the bullet. Just like your 38 is "38 Special", but there is also 38 Super, 38 S&W, 38 Long Colt, 38 Short Colt, etc. etc., there is 9x17mm, 9x18mm, 9x19mm, 9x21mm, 9x23mm, etc. etc.
380, which is the round the PPK is chambered in, is also known in Europe as 9x18mm and 9mm Browning Short.
So it is true the 380 will shoot 9mm. Just not 9mm Luger.