Stuffed in between "skill challenges" and "traps and hazards" in the 4e DMG is a potential third kind of "noncombat encounter": puzzles. (Of course, all three are reducible to the first kind.)
"Puzzles in a D&D game," according to 4e, "present a unique form of challenge, one that tests the capabilities of the players at the table instead of their characters." The paragraph goes on to identify combat, traps and skill challenges as involving plenty of die rolling.
"Furthermore, puzzles present a challenge to players that's usually independent of their experience with the game." There is indeed a degree to which skill is not synonymous with experience, even in matters dealing directly with peculiarities of the game. Some people learn more quickly than others. I have seen common sense trump purely rules-focused "tactical expertise" often enough. That said, experience at problem solving can be as instructive if arrived at in the game as without.
"The basic nature of puzzles -- that they rely on player ability -- is the reason that some people love puzzles in the game and some people dislike them." Some wisdom there, perhaps? And maybe not just coincidence that different games have been designed with different emphases?
Rather curiously (to an old hand), this is as close as the "Noncombat Encounters" chapter gets to treating what I would call a plain role-playing interaction with a character, or with any aspect of the environment. The apparent reason is in technical redefinition of old D&D terminology: "An encounter, by definition, involves a meaningful risk of failure." Just what that means is suggested in that other puzzles "might be obstacles in the characters' path, but ones they can find other ways around. As a rule of thumb, you can treat a puzzle as an encounter if there's a definite time limit or other serious risk to failing to solve the puzzle in that time. Otherwise, it's not an encounter." (Emphasis added.)
And, of course, "you can always set up a puzzle as a skill challenge." That would make it a non-puzzle, by the earlier definition, but what the hey.