I'm going to sound crazy, but what all does a programmer do?

There are some in-depth descriptions of the various roles over on Tom Sloper's site. They look like items 1, 4, 5, 7, 10, 15, 17, 24, 31, and a few others. I recommend reading all the articles on his list, there are many great entries.

Game designer - Could be gameplay/mechanics design, story design, level design, and any thing to do with what the game is about and or whats in the game.

Programmer - Implements game designers ideas and creates a game from them, this includes, audio, graphics, mechanics, ai, ui, systems, tools, build engineers.

Artist - Creates the visual assets for the game, modeling, ui art, texturing, concept art, 2d art.

Game designer - Could be gameplay/mechanics design, story design, level design, and any thing to do with what the game is about and or whats in the game.

'Game designer' is generic term, that's not fully defined and may vary from studio to studio.

Just because someone is a "game designer", that doesn't mean they'll do level design (the level designers or even 3D modellers probably do that), or story design (the writers would handle that).

A "game designer" doesn't necessarily get to dictate what the story is or how the levels are laid out.

Obviously responsibilities vary between companies and depend on the size of a project; working on your own project, you get to be everything. Working on a project for Activision for example, your responsibilities will be alot more specific.

If you want to design levels, setting out to be a "game designer" might be the wrong path. If you want to write for games, becoming a writer might be a better route to take.

I think the idea of a position where you are given a hundred-million-dollar budget and a list of peons to implement every whim of an idea you have is probably illusionary - unless the multimillion-dollar budget comes out of your own wallet or you own the studio. I think the term 'game designer' holds alot more fantasy in people's minds than the reality of it might actually be; but I could definitely be mistaken, seeing as I'm not in the industry myself.