Is a DS game ';box'; the same as the ';case';?

I just bought a used copy of Tetris DS, and I noticed that many sellers say they have the box with instructions. But then I see sellers saying they have the ';case'; with instructions. Is the game case same as a game box? I am just paranoid I am getting some plastic game holder in stead of the original game case.Is a DS game ';box'; the same as the ';case';?
Cases and boxes are the same things but it still might not be in the original game case.Is a DS game ';box'; the same as the ';case';?
Its all the same people just call it by different names most commonly its called a case.