Ah dear potato, king of vegetable!
I am not that much aware of the exact properties of the dozen variety my country has, much less the hundreds there are in the world.
But where I live they are conveniently sorted depending on their properties, mostly starch content and size.
Size matters if you want to cook them whole, peeled or not. As if they are too big they will tend to crack due to the required prolonged cooking time.
Starch content is important depending if you want them to be firm or to dissolve:
-starch rich potatoes are ideal for things such as mashed potatoes, gratin dauphinois, or to enrich a soup or stew.
-potatoes with less starch tend to be firmer, and so are ideal for salad, or when you want to add chunks of potato in a dish, or "firm" potato dishes such as spanish tortilla or roesti.
Young or precocious potatoes, small sized and firm, are a delish cooked whole with their skin, accompanying meat or cheese (Raclette or even Fondue

).