Potatoes

They are great stuff, and come in many varieties. The indigenous people of the Andes know more kinds than our supermarkets will ever offer.
Here in Germany, the varieties are sorted into three categories that have a different starch composition which gives them different cooking characteristics:

1. "festkochend" (meaning "firm when cooked"), also called "Salad potatoes"
As their name indicates, they stay firm even when fully cooked. That takes longer than with the other varieties, too.
When cut up after cooking, they retain their shape and edges, which makes them ideal for salads because they don't break up. If you use them for mashed potatoes, however, you will always have some small lumps in the mash (which could of course be a desired effect)

2. "vorwiegend festkochend" (mostly firm when cooked)
They are the most versatile, standard variety. The can be used for boiled potatoes (peeled either before or after cooking), baked potatoes, fries, roast potatoes, mash...
They break up when sliced, however, so they are not the preferred choice for potato salads. Also, you cannot make Swiss "rösti" with them or other dishes like Italian "gnocchi" where starch needs to leach out to keep the dish together.

3. "mehlig kochend" (literally: cooking to flour)
Those varieties give up a lot of starch when they're cooked, and the pieces tend to stick together.
This is desired when making some special dishes, as mentioned above. Also, these potatoes fall apart easily and so they are the perfect choice for mash

Friends who have been living in China as expatriates have told us they didn't cook potatoes there: the merchants mixed the different varieties. Whenever they cooked them, they ended up with a mix of mash and firm potatoes, and that wasn't very palatable!