They sort of run into each other. The online dictionary at uio uses idrett to explain sport and vise versa. I think it's more common to use -sport when using collective terms like ballsport (all sports using a ball), skøytesport (all sports on skates) etc.
I would ask someone of they were doing idrett and ask if they liked watching sport. But not consistently...
"Idrett" and "sport" are not completely synonymous in Norwegian, though there is quite some overlap.
"Idrett" is mainly used for sports where the physical prowess of the athlete is in focus; sports which require a great deal of strength, agility and/or stamina, and where the participants rely primarily on themselves and their team to win.
Sports like golf or sailing, which also require physical skill, but where gear and other factors play a greater part, are more often referred to as "sport". "Sport" is also used as a general term when referring to both types of sports collectively.