Who was the first Swede in the NHL?
Gus Forslund was the first Sweden-born player, Ulf Sterner arrived from Swedish hockey and Thommie Bergman established an NHL place. Three different milestones.
Gus Forslund was the first Sweden-born NHL player, appearing for the Ottawa Senators in 1932/33. Ulf Sterner became the first European-born and European-trained NHL player in 1965. Thommie Bergman established a regular NHL place in 1972. The answer depends on which milestone the question describes.
Gus Forslund: born in Sweden, raised in Canada
Forslund was born in Sweden but grew up in Canada. His route to the NHL ran through North American hockey rather than a move from a Swedish club.
He played 48 regular-season games for Ottawa in 1932/33. The NHL's historical records list 4 goals. This was the original Senators franchise, not the club that entered the league in 1992.
Ulf Sterner: the European-trained pioneer
Sterner made his Rangers debut on January 27, 1965. He arrived from Swedish hockey, while Forslund had grown up and learned the game in Canada. The Rangers' account identifies him as the first NHL player born and trained in Europe.
He played 4 NHL games. That was a landmark debut, but not the start of a permanent NHL place.
Thommie Bergman: establishing a regular place
Bergman joined Detroit in 1972 and became a regular NHL player after developing in Swedish hockey. That distinction explains why Swedish accounts also describe him as a first. The NHL's Swedish pioneer profile makes the context clear.
What about Börje Salming and Sven Tumba?
Börje Salming and Inge Hammarström arrived in Toronto in 1973, after Bergman's first season in Detroit.
Tumba tried out in Boston without securing a regular NHL place. A tryout is not an official NHL appearance. The NHL's later Bergman profile sets out the distinctions.