I think the biggest distinction is that in addition to pork bones, they also add chicken bones and vegetables to the broth to make it richer. Also, they add pepper oil and garlic as topping. The raw egg yolks are not part of the style, they’re an “unorthodox” (because it deviates from the traditional style), but delicious addition by the restaurant.
In my experience, this is because they conduct yearly x-ray examinations to detect tuberculosis and other lung diseases. Shirts and bras interfere with the image, so they ask students to bring a plain shirt to wear during the examination. However, if there’s no other option, they may ask them to do the examination bare-chested. In my case, there was gender separation (not only in location but also in the time frame), but I can’t say the same for all schools or age groups. Japanese schools are known for having students change into sports clothing in the classroom without gender separation up to 3rd or 4th grade, so I wouldn’t be surprised if there are schools that don’t separate genders for medical examinations.