The Skolt nation, the true woodland Sa'ami, lived in general from about where the Norwegian/Russian border is today, across to Penchanga and then down to Lake Inari and east to what is the Russian/Finnish border regions.
The Pomars, also reindeer chasing people, but of Slavic origin ~ usually identified as Russian by most sources, competed for the same sort of range in the Eastern reaches, or Fenns/Finns of Finland.
The Pmars and Sa'ami are clearly identifiable from the standpoint of modern Finns.
Still, when the term "Finn" was ascribed principally to the people living in the Finmark ~ in the North Everywhere, the people who actually lived there were Sa'ami.
The ships logs kept by the Swedes (which ever ones we can find) identified the LANGUAGE spoken by the people on board the book ~ and Sa'ami were always identified as FIN.
It is possible there were a couple of "Finns" somewhere ~ 'cause there's the town of Finland in Lanaster County PA ~ it dates from an early time. It's right up the road from Nickelmines ~ originally settled by Sa'ami from what is now Petsamo Oblast
Only Germans and English people live there now, all the Scandinavians having moved out to avoid disturbances by Quakers.
Otherwise there are many places whose names contain the word "deer" or "union", and they are places established later by Sa'ami who were only lightly supervised, counseled, or ruled over by anyone!
The Skolt Sa'ami were clearly REMOVED from most of their territory in Northern Finland and Russia by Swedes and Russians more interested in the iron ore, and the nickel mines than in people selling baskets and deer hide.
At some point in time it became conventional to refer to the various Scandinavan, Russian and Latvian/Estonian tribesmen living in Finland as Finns.
Before that time Finn was the description of the language and place where the Sa'ami lived.