Not really, unless you can find a contrasting definition to one found on WorldReference. Puncture is defined as making a hole in surface (the boundary) rather a volume (the solid). In any case this goes off topic. You've apparently misunderstood what people usually mean with hole. (edit: Or maybe I've. Now I'm confused. Here goes the rest of my day thinking about the meaning of holes.)

There are no holes that puncture the ground. All holes in the ground are, in your terminology, "valleys".

A puncture is a hole, and vice versa. These are synonyms.

How many holes are there in a coffee mug?

Septillions, especially if there's coffee in it.