I don't think the NHL has stronger and faster players than the SHL. I think the NHL plays a more physical brand than the SHL, especially since the ice is much narrower. And because the ice is narrower, events happen much faster - not that players are faster. If a player can't skate well or fast in the SHL, then he will be exposed.
Carlsson did display some hits in the SHL, but you can witness his physicality more when he's trying to secure the puck when he's using his body. Often in a race for a loose puck, Carlsson will use his body to gain space advantage than trying to win the puck by skating fast to it. He does it in the NHL too when you see him push players off in order to win puck possession for a loose puck.
Leo does so many subtle things well that lead to splashy plays. I wish more of our players were that attentive in executing all the little things.