> When most people say "immigrate", they are not referring to foreign worker status that allows for long term residency, but actual naturalization.
It depends on how the country defines it, but to "immigrate" doesn't generally mean naturalization.
Immigration means to obtain permanent residency (in the U.S., a green card or LPR status; in Canada, Australia, NZ, landed immigrant or permanent resident status; in the UK, indefinitely leave to remain). Permanent residency generally confers most rights of citizenship, apart from a few like the right to hold a passport of that country, to vote (exceptions exist), etc.
Naturalization means to obtain full citizenship. It's the step that comes after immigration, and it is optional. Not all immigrants elect to naturalize for various reasons (e.g. wanting to keep original citizenship in cases where dual citizenship is prohibited, tax rules, military service, etc.). Some choose to remain permanent residents forever, and they can. It's their choice.
And you're right -- if someone has a temporary status like a foreign worker status (even if it's infinitely renewable), that would be considered neither immigration nor naturalization.
I'm not sure how things work in Japan, but it is possible for a country to be easy to immigrate into, but hard to naturalize in. These two things can be simultaneously true.
(in other words, easy to get permanent resident status, but hard to get citizenship)