P38 Question

First let me say I know nothing about Lugers, with that out of the way I will now ask some stupid questions.

Is a P38 a Luger? I have a K98 with Nazi markings and would like a Luger with Nazi markings (mostly just to have, but still would like it to be functional)I noticed century has A like new P38 for 599.87 in 9mm (is this the caliber the Germans used).

Thanks for any guidance you can offer.

Tim