While Programming requires you brain to think, Game design requires you brain to be creative
i actually agree with this, although i see why others are challenging how you stated it. they're definitely two distinct things
programming is a logical creativity, because what you have to work with are tools like if-statements, variables, values etc. that are as fundamentally concrete as say... mathematics
game design can be thought of as something larger that captures programming, as well as something much less concrete. it's a general creativity, because you have to consider how the code, the art, the sound, how everything ties together
for example, there are tons of different ways to program player movement into a game. you might decide to you want the player to slide, jump, roll, and all this other advanced tech. or maybe you only need to be able to walk left and right and nothing else. deciding what type of movement to use is part of design, but once you've
designed the movement system, you get down to programming it.
the wikipedia pages related to all these areas, like
game design, help make the distinction even more clear. remember that "game" doesn't just apply to what you play on a computer. game design exists for board games, card games, and even sports games, where programming would never be a part of the development process.