There is a whole vocabulary to describe the different types and tastes of these stone roasted potatoes. The menu of the stall pictured below lists four main types: tomitsu-red from Fukui (top left), milk-sweet-silk (top right), murasaki-imo as described earlier (bottom right), and another type of tomitsu from Fukui (which is obscured by a note saying "now roasting/curing - please wait!). The taste/texture of each potato is also given:hokkori (from hokuhoku describing the fibrous fluffy soft potato texture); shittori (moist?); nettori (creamy, sticky); mitsu (honey); and kaori (fragrant). Note the halal mark to the left of the menu and the English sign saying (I quote), "No add any sugar, only baking. Magical sweetness in here." Couldn't have said it better myself.
Sweet potatoes find their way into a huge variety of products that Japanese love. One example is shōchū; although usually made from the fermentation of rice this Japanese spirit also has a sweet potato version (known as imo-jōchū). Moreover, the natural sweetness of the satsuma-imo naturally lends itself to sweets and confectionery. One best seller is purple sweet potato ice-cream: Häagen Daz' limited edition (kikan gentei =期間限定) murasaki-imo (紫いも) ice-cream was unbelievably popular (for a recipe see here). And it doesn't end there. This site lists a variety of interesting ways Japanese use sweet potatoes as a key ingredient in sweets, including kit-kats, tarts, milk-shakes, cookies, chocolates, and various other snacks. Magical sweetness indeed!