Finnish, Estonian and Hungarian are closely related languages. This is a result of history. The Sa'ami languages are NOT closely related as languages go, but they are far more ancient than Finnish, Estonian, Hungarian or the various Indo-European dialects like English, German, Romanian and Tocharian.
For a very long time there's been a debate about whether or not the Sa'ami languages were just variations on Finnish, or had their own source ~ maybe somewhere in the far east. In those days the greatest scientists on earth thought all the Sa'ami originated in the East ~ mostly because of differences in their cheekbones and their eyes ~ like Blond Mongols!
DNA revealed the Sa'ami to be wholly European in origin ~ just the first people to leave the Western European refugia as the Big Ice began melting. They went due North and presumably were heavy into seafood. Eventually they spent the next 19,000 years fairly isolated from other Europeans and retained many features that make them look like the Eastern peoples who split off from the Europeans between 58,000 and 35,000 years back (even the Chinese are not genetically isolated from Europeans more than 35,000 years.)
There was one "meeting" with an outside population about 7,000 to 8,000 years ago so the Eastern Sa'ami managed to pick up some Eastern European DNA ~ and with that managed to introduce some Sa'ami linguistic elements into the blends that ultimately became Hungarian, Estonian and Finnish. Later contact with the Mongols added yet more words to their vocabulary in the 1300s BTW. But even before then, the current thesis is that Sa'ami languages probably lent many of the basic grammatical terms to the less developed Eastern European and Asiatic languages. NOTE: that was all going on before there were any clearly identifiable Indo-European languages.
Within the context of the period from 8,000 years back until about 560 AD, much of the basic Eastern Sa'ami language base got transmitted to East Central Siberia ~ where all the American Indians, East Asians, Japanese, etc. originate. This is in the plains North of the Gobi ~ prime hunting area in the aftermath of the Ice Age.
Not much credit was given to the idea that the Sa'ami actually got that far themselves ~ so the anthropologists had hypothetical East Asian hunters trudging back and forth across the Steppes swapping tusks with the Sa'ami and getting dried reindeer meat in return.
Then within the last 10 years DNA studies revealed a gene sequence called the X-Factor present exclusively in the Sa'ami. Then they found the X-Factor in the Chippewa, then the Cherokee, then the Iroquois, Delaware, Fulbe (in Africa), the Berber (in North Africa), and voila, the Yakuts Sakha in East Central Siberia.
The Yakuts Sakha have a written record recently translated that reports on their recurring invasions of Eastern India, and their returns to Siberia ~ depending on climate, how upset the native got, and so forth, they were there ~ one of their most famous members is known as Buddha. That's why he looks pretty Asian!
About 535 the climate in Western Europe, Eastern Europe, Northern Asia, and a wide variety of other places turned very bad and a Dark Age began in the affected places. Economies collapsed elsewhere.
That's when the Yakuts Sakha traveled East and conquered much of Korea, and much of Japan ~ however, the war in Japan lasted until the 1500s.
I don't think the noble classes in Japan have had their DNA checked for the X-Factor gene sequence, but I wouldn't bet against it being there.
The Yakuts Sakha imposed their Turcic language on Korea and Japan. It has strong elements of the other better known Mongolian languages, but there are Sa'ami words in there ~ just like there are Sa'ami words in all the Indo-European dialects, and all the other Uralic or Altaic languages, particularly Finnish.
Beyond that it's hard to say why lake Inari means a type of sushi in Japanese ~ but it may have to do with FISH.
Thank you. That is extremely interesting.