I can only give you my experience (working as a civil servant, teaching English in a public high school). People generally have 20 days of vacation and 20 days of sick leave per year. You can get more sick leave if there is a good reason (i.e. if you are hospitalised), but at some point I think disability kicks in. I can tell you (since I now have my own company) that disability insurance is private, so the details will vary. There is also no requirement for an employer to have disability insurance, although I'm pretty sure they do in the government (I had a couple of friends on disability for a couple of years).

Generally speaking, people do not take time off in their first year of employment (either vacation time of sick leave). If you are very ill, you need to go to the doctor and get a note. This includes the flu. Basically, you go to the doctor and if the doctor thinks there is a chance that you might have the flu, then you you'll get a note.

People go to the doctor when they even just have the sniffles. There are clinics everywhere and walk in appointments are the norm. You just go in, fill in forms (if you aren't already a patient there), wait for an hour or so, talk to the doctor for 10 minutes and then leave. If the doctor says you shouldn't go to work, then "It can't be helped" and you can't go to work. Pretty much that's the end of it.

However it can get more complicated than that. If you are ill a lot, you will generally get some criticism. Your presence is considered necessary and so if you aren't there, then other people have to put in extra work (whether that's really true or not depends on the job, I guess). Most people will use a vacation day rather than a sick day if they are ill. However, that's in the context that people don't generally use all their vacation days, so it's pretty difficult to say.

For me, I underwent minor surgery while I was working at the school and took 2 sick days (one to go to the hospital when I was very ill and one to have the surgery). One of my colleagues complained, but my department head protected me. Probably sounds very weird, right? But that's the way it is. Me taking a day off meant more work for the colleague, but the department head decided it would be better in the long run if I didn't die ;-)

Again, I have to stress that the time off thing is very different than other places. When I got married, I went to my department head to see if there was a way I could take a day off. He said, "Absolutely. Would you like the morning or afternoon off?" I ended up getting married on a public holiday.

I had a colleague who had a bad back (he used to be a pro wrestler in Mexico of all things -- Japanese guy). He had to have a ton of surgery (over several years). He was gone at least 6 months without going on disability, but then eventually the school had to ask him to go on disability so that they could hire a temporary replacement. On the other extreme, I knew someone with cancer who had to go for regular treatments and the school asked if there was some way he could schedule his treatments so that they didn't interfere with his work schedule. So it's not at all what you might imagine (either one way or the other). Sometimes they bend over backwards to help you out and sometimes they make seemingly petty demands. It depends a lot on your management and the organisation. And sometimes it even depends on your colleagues because if they complain about you a lot, then the department head has to do something to fix the problem. In Japan, forcing your department head to fix a problem is pretty well the best way to get in their bad books -- you are supposed to take responsibility and find solutions to problems yourself.

And I think that last sentence really sums up my experience with that kind of thing in Japan. Creating problems (even if they aren't your fault) that others have to fix is just tremendously bad form. This puts a lot of pressure on you do find a solution -- and often that solution is "I'll go to work even if I'm ill".