Besides the point made above about the provenance of "National Insurance," I'd also like to inject a note of caution with respect to Japanese terminology.
Kokumin nenkin only refers to one part of the Japanese pension system, so it shouldn't be taken to mean "the Japanese state pension" or the equivalent of US Social Security without an awareness of the qualifications involved. Such an awareness is necessary if comparisons with the pension systems of other countries are to be more than just rough approximations.
In particular, it is important to recognize the distinction between the two tiers of the Japanese public-pension system:
kokumin nenkin and
kōsei nenkin. The Japan Pension Service refers in English to the two tiers of its public-pension system as the
National Pension system and the
Employees' Pension Insurance (EPI) system. Technically, the National Pension incorporates several components -- including disability benefits and survivors' benefits -- of which the Old-Age Basic Pension (
rōrei kiso nenkin, or
kiso nenkin for short) is the actual old-age pension. Likewise, EPI incorporates -- in addition to other benefits -- both an Old-Age Basic Pension component and an Old-Age Employees' Pension (
rōrei kōsei nenkin, or
kōsei nenkin for short) component (see the concise Japanese definitions
here.) The Employees' Pension, unlike the National Pension, is earnings-based, has significantly different contribution requirements, and provides significantly different benefits.
The two schemes are thus joined at the hip, so to speak, but the National Pension is categorical different from the Employees' Pension, and the only way to refer to both together is to use the term
kōteki nenkin, or public pension(s). You will simply not see
kokumin nenkin used to include
kōsei nenkin -- which in the narrowest sense means only the Old-Age Employees' Pension component of the pension -- anywhere in Japanese.
So with regard to "state pension," I would take
kokumin nenkin to be more limited in scope (though I'm not familiar with the pension systems of most countries and YMMV). With regard to Social Security, that system is wholly earnings-based, so it does not really correspond to
kokumin nenkin at all -- it corresponds more closely to
kōsei nenkin, especially in the narrow sense of the term, although it can be useful at times to describe it as roughly equivalent to
kōteki nenkin.
By the way, one of the quirks of this two-tier system (and another indication of the distinction between the tiers) is that even though an employee is no longer covered by the Basic Pension after age 60, Employees' Pension premiums -- being calculated holistically based on income -- are not reduced. In other words, your premiums stay the same (depending on salary), but you generally receive no further Basic Pension benefits. You can also choose to take or delay receiving either component independently.
