There are hundreds of kinds of tofu here in Japan. That's why I love calling it Tofuland. Well, hundreds of kinds might be an exaggeration, but it might actually be true. I haven't tried all of them, but I have tried a lot. And from my experience, I would like to categorize it into three general kinds.
The first two types, you've probably heard or read it several times before, are kinugoshi tofu (silken tofu) and momen tofu (firm tofu). Before coming to Japan, I had an impression that silken tofu is the "high quality" type of tofu. It was expensive in Manila and you cannot buy it anywhere in my hometown; that's why I never got the courage to try making a vegan dessert mousse, afraid that I might end up wasting the expensive tofu. When I got here, I understood that to make kinugoshi or silken tofu, soy curd is strained on silk cloth. Kinu means "silk", and kinugoshi means "straining through silk cloth". Momen or firm tofu, on the other hand, is strained using a cloth made of cotton. Momen also means "cotton". I don't understand exactly how, but kinugoshi tofu has more water content than momen tofu. But still, my husband prefers kinugoshi tofu because of its texture, so this is what is usually in our fridge.
These two types, kinugoshi/silken and momen/firm tofu, still have numerous variations: from tofu (usually kinugoshi) with extracts from yuzu fruit or edamame or whatever, to firm kinugoshi tofu, to special high quality kinugoshi tofu, to tofu (usually momen) that are mixed with different seasonings or flavors (like the type for tofu steak), and many more.
Most vegetarians know that the by-product of tofu is soy pulp (see pictures above). They call it okara or u-no-hana here. I have never seen it sold in supermarkets except here in Tofuland. They sell it as fresh pulp, and recently, I saw a powder form of it that you can add to drinks, soups, yogurt and everything. The third kind of tofu is deep-fried tofu (or aburaage in Japanese). Yes, like a fantasy come true, tofu is sold already fried here. And what's more, the variety of deep-fried tofu is so well-thought of, that I have never yet deep-fried tofu at home. Well, except for my cornstarch-coated tofu tempura.
If you need thinly fried tofu, usuage is what you're looking for. It gets crunchy when you put it on a hot nonstick pan without oil (like in this dish cooked by my husband) or it becomes a sponge that spurts out sauces of dishes like pad Thai or soups (miso soup!)! The word usuage means "thinly deep-fried" (usui = thin, age = deep-fried). However, if you want thick fried tofu for tofu dish like Worcester sauce tofu, curry, and kombu tofu, what you're looking for is atsuage (atsui = thick, age = deep-fried)
There's another kind of deep-fried tofu-- the one with different kinds of thinly sliced vegetables and are usually round in shape called ganmo (see pictures above). I like just boiling this one in mirin, soy sauce and kombu powder (and sake, for my husband) and putting it in his bento. So, that's currently all I know about tofu (that's made of soy beans), I guess. If you know more about them, please do share it to us in the comments or if you have questions, I would gladly answer them (or research about them if I don't know the answer too). Tofu to fun!