(Norrland isn't a province. It's one of three regions of Sweden, roughly the two northern thirds of the country by area, containing nine of the twenty-five traditional provinces.)
This is further complicated by the fact that Sweden is divided into 21 administrative units (the twenty-five traditional provinces are non-administrative units), in Swedish called "regioner" (formerly "landsting"), where five of these are situated in Norrland.
Area-wise Norrland is roughly 60% of Sweden’s total area[1], while Montana is less than 4% of the US total area. I think that makes the comparison more fair.
Finland was historically a part of Sweden for about 600 years, and the northernmost part was called Lapland. Nowadays that part is split into Swedish Lapland and Finnish Lapland. Norrland (literally "northern land") is the name for the part of Sweden that is north of approximately 61 degrees northern latitude, so it includes Swedish Lapland but also a lot more.
Lapland is a historical province in Sweden. You'll also find a northernmost part of Finland with the same name: https://en.wikipedia.org/wiki/Lapland
One area around three national parts (Padjelanta, Sarek, Stora sjöfallet) is also called Laponia.
But the political division of Sweden around that area - that's Norbottens län, so that's the subdivision that people care most about in their day-to-day life.
Norr means ”north”. Norrland is the Northern 2/3 of the country. It’s not formally defined but more like the “Midwest” and similar. Lapland is a part of Norrland.
Lappland is a part of Norrland, but both of these terms are used in a historical sense as cultural/geographical regions, and nowadays replaced by counties
