Baking is more of a evaporation.
And the german definition of cooking in the narrow sense is defined like this, but in a broader sense apparently usable for everything with preparing meals.
And I never used a rice cooker, so no idea how to classify that ..
To the rice cooker point, I'd argue that an oven uses a heating element of some form (electric coils, gas flame, wood fire) to heat the air in a closed environment, and the air transfers heat into an item. In contrast, a rice cooker uses a heating element to directly heat a metal pot, and the metal pot transfers heat into an item. Usually that's going to be a combination of rice and water, but you can e.g. pour pancake batter into the pot and get a large souffle pancake, or put bread dough into the pot and get a loaf of bread. The trick is that the metal pot is much more efficient at transferring heat than the air is, so the rice cooker doesn't need to be at the same temperature as an oven to get the same amount of heat into whatever you're cooking.
In german you would not, one would roast it. (but we have 2 words, roasting "rösten" on the bbq and "braten" would be in a pan. But a "Braten" would be in an oven.)
Kind of not that consistent (like it usually is with natural language).
In general I think those terms were invented, before there were things as a rice cooker.