The main difference is that soybeans are used to make tofu and tempeh, whereas edamame (soybean pods) are eaten boiled.
The second thing you can do with soybeans is make your own miso, which is a fermented bean paste. Miso is usually made from soybeans, but it can also be made from other legumes, such as chickpeas, mung beans, or adzuki beans.
There are a variety of ways to make miso, but most begin by soaking the soybeans in water for about 24 hours, then boiling them for about 10 minutes, then adding the rest of the ingredients and fermenting them for anywhere from 1 week to a month. Soy sauce is another fermented product made from soybeans.