The 'AP' shells used by smaller warships weren't truly Armor Piercing, but what the British called 'Common', or 'Semi-Armor Piercing'. They were designed to penetrate about half what a normal AP shell of the same size would do. The smallest true AP shells anybody made were for 6" (150mm) guns, and even those were rare in World War Two.
And more: an AP shell has more of its weight taken up by the armor-piercing cap, so it has a lot less powder than an SAP or HE shell. It should go through more armor but make a smaller bang. And of course a 3.46" (8.8cm) shell is not going to penetrate the armor on a light cruiser, much less a battleship.
I hope that helps some.
