Before we go too much further with this, I should point out that I explain this system to clients' incoming foreign employees as part of my job.
The only thing we differ in our explanations is that you think shakai hoken equals to only kenko hoken, kosei nenkin and koyohoken. This is not correct as shakai hoken is a more broader term and means in general the combination of medical insurance, pension and disability insurance.
You just said (with my additions in italics), "you think shakai hoken equals to only kenko hoken
(aka medical insurance), kosei nenkin
(aka employee pension) and koyohoken
(aka employment/disability insurance)"
then followed with
"shakai hoken is a more broader term and means in general the combination of medical insurance, pension and disability insurance. [/quote]"
I'm not sure where you think the difference is here, but you seem to think that "shakai hoken" equates to a general term for "social insurance". It does not - shakai hoken is a specific government social insurance scheme, with specific components and benefits.
[/quote]So then for example kenko hoken and kokumin kenko hoken are interchangeable parts of shakai hoken [/quote]
No they are not. You are enrolled in
one or the other, never both. If you are self employed, a low-hours part time worker, or unemployed, you are not eligible for coverage under shakai hoken or shigaku kyousai. Kokumin kenko hoken is the system for people who are not eligibile for coverage under those schemes, and is not part of shakai hoken, at all. It states quite clearly in the page you linked: "会社勤めの人なら
「健康保険」、自営業者・短時間労働者・無職の人などは
「国民健康保険」に加入することになります。"
as are kosei nenkin and kokumin nenkin (though with that you can also participate in both).
Pretty simple description can be found for example here:
https://hoken.azukichi.net/shaho.html
They are separate. Again, says so in the page you linked. "会社勤めの人なら
「厚生年金保険」、自営業者・短時間労働者・無職の人などは
「国民年金」に加入することになります。"
Here's a fairly comprehensive explanation in English for you -
http://www.nic-nagoya.or.jp/en/e/archives/4775