But What Kind?

This evening GLH and I ate at a lovely restaurant serving traditional Swiss fare. Along with GLH's entree, he had a choice of several different kinds of potatoes. Two of the potato options were unknown to us.

Our waiter spoke some English. But we think the meaning was lost in translation.

Here is the conversation:

Me: I know that "pommes" means potatoes. But what are "Pommes Williams" and "Pommes Duchesses?"

Waiter: They are potatoes.

Me: I understand they are potatoes. But what else is in them?

Waiter: Potatoes.

Me: How are the potatoes made?

Waiter (pointing at menu): These potatoes are made one way and these are made another.

I gave up...