While they preferred handguns chambered in 9mm or .380
Actually, for what its worth, the Germans did NOT prefer 380 at all. It was a non standard caliber for the Wehrmacht. They primarily had 9mm or 32 acp. 380s were made and or issued in much smaller numbers.
As the war drug on, the Germans began using about any decent handguns they could get their hands on. I suspect that the main reason that they used so many .32's is because there were simply a lot of arms factories in countries like Czechoslovakia, Yugoslavia, Poland, and others that they invaded that were already tooled up to make .32 semi-autos.
I am reminded of an interesting story I once heard. An acquantence of my dad's worked as a hospital security guard several years ago and was allowed to carry a gun while on the job. What he chose to carry was an Erma .25 Auto that he'd picked up inexpensively in a pawn shop and one day he decided to take it apart in the break room and was having trouble getting it back together. While mulling over his situation, an older doctor that had immigrated from Germany noticed the gun and asked if he could give it a try. Much to the security guard's surprise, the doctor assembled the gun quite easily and quickly. Upon asking how he knew so much about the gun, the doctor replied that he'd been a physician in the German Army during WWII and was issued the same type of gun for a personal defense weapon.