There's a world of variety among the toilets you can find in Japan. I never thought a visit to the commode could offer so much, but it has been an education.
First off, for the truly scornful breed of you, the cherished piss-pot is not even necessary. You can whip it out and throw it down wherever you happen to feel the yellow-eyed need. It's not uncommon to see a Japanese man staring at a wall, or simply the unsuspecting passers by, while holding himself. I'm glad to see tradition rear its head, even when there appears to be a lack of a head readily available.
Moving to more discreet methods of disposal. It's not hard to find those upright urinals built into or onto walls in restaurant or office bathrooms, perhaps more common in modern buildings. In many bars and older buildings, the urinal is a flat receptacle, like a mini wall-urinal, built into the floor. Sort of a fancy hole in the ground. I've never used one for anything more complicated than urination, being unpracticed at the other and fearing my own clumsiness. I haven't come across any of those trough-style urinals that you can find at many coliseums or sports arenas in the states. Also, many public bathrooms just don't have doors. It's not unusual to pass by a park and check the package of anyone who might be taking advantage of such a handy lavatory. So much for discretion.
Now, you can find the "Western-style" toilets, like those porcelain jobbers that we have in the states, in many places. We have one in our apartment, for example. In a gadget nation like Japan, they have, of course, improved upon it. Many "Western-style" toilets here include a control panel! Imagine flying a spaceshit while unloading your cargo. One button keeps the seat warm, which is a great feature during the Winter. It's hard to say what the other buttons do. Fortunately, I can't read much Japanese, but many of the icons on the toilet's dashboard are quite telling, as well as useful to the illiterate.
Recently, I discovered a new model. Upon entering a stall, I was pleased to discover that someone had, I thought, placed a paper seat cover on the seat and then, for whatever reason, left. I was happy about not having to touch anything else and went about my business. Anyway, having made use of a public repository and then flushing away the seat cover, a new paper seat cover emerged from what looked like a printer attached to the back of the toilet. This was an invention to marvel!