There seems to be a lot of confusion -- some of it deliberate, unfortunately -- about several categories of academic programs devoted to games. I'm going to try to describe the differences between "game studies," "game development/production," and "game design."
In "game studies" you are not creating games or even ideas or frameworks for games. You are studying and analyzing games and game players the way psychologists study people or biologists study plants and animals. You want to know such things as why people play games, what "fun" is, what are the fundamental elements of games, what role story plays in games; you may spend a lot of time and effort defining just what a game is -- and never come to a conclusion all can agree on!
Another aspect of game studies can be evaluating the effect of game playing on the players (for example, with educational games and simulations). The person studying games may not be a lifelong avid game player, though I'd think that many are. Someone in game studies, when playing or watching a game, is more likely to think about how it works, to analyze it, to consider how it affects the players, than he is to be concerned about how enjoyable it is to play (though that IS part of the analysis). The principle "deliverables" of game studies students -- what they actually make or do -- are long academic papers about games.
Sometimes the study of games is called "ludology", and as with any other academic discipline, there are doctoral dissertations and formal journals and conferences devoted to the study of games.
Game studies people ponder; game developers and game designers do. As with many academic disciplines, then, game studies can ultimately illuminate how games can be improved, but its effects on game creation are indirect and distant rather than direct. If you want to actually make games, "game studies" is not where you want to be.
In video game development, your concern is how to create the entire game, to get from the image of the game originally residing in the mind of the designer(s) -- the initial game design -- to a working video game. (A better term would be video game production or video game creation.) The great part of the production time and money is devoted to programming and art, with lesser amounts spent on game design.
A school teaching game development, then, may concentrate on one of the aspects, or may try to cover the three major ones, design, programming, and art.
In contrast, in the non-electronic game world, game development plays a fairly small part in the creation of a game, because there is no programming, no sound, and so forth. The art is simple, and there is rarely much of it. A published non-electronic game is 80 to 95 percent the work of the designer, whereas a AAA list video game is perhaps 25 percent the work of the design team (such games are designed by committee, in effect, if not formally).
A video game developer who is not a designer, when playing or watching a game, is likely to think about how it how it was made, what software tools were used, how long it took, how many people were involved. But developers usually love to play games, as well.
The "deliverables" of game development students, depending on their concentration, will be 3D models, animation, artwork, pieces of game programs, mods, fully-realized simple video games (no one has the time to make a AAA list style game in school).
This brings us to game design. The game designer is the person who conceives the framework and structure of a game, who writes the rules or the game design document for the game, who decides how to modify the prototype many times until, ideally, the game is good enough to be manufactured.
Game design is a combination of conception, communication, and dogged continuous improvement, via playtesting. The initial ideas don't count for much, and anyone who thinks he can get an idea and someone else will do the real work is in cloudcuckoo land.
In video games, constant communication is very important, as other people actually make the game and get it to work. The designer has to describe his game in great detail so that those people can make it. (In the non-electronic world, the designer makes the entire game, except for the actual production artwork. Communication with play testers and publishers is still important.)
In many cases, AAA list video games are actually designed by committee, involving several official "designers" but also every person on the production team. Everyone wants to contribute to how the game works, and the designer must carefully accommodate (and take advantage of the brain power of) all those folks.
A video game designer, when playing or watching a game, is likely to think about player interaction, challenges, what makes the game worth playing.
The "deliverables" of game design students are completed non-electronic games, completed levels for existing games, completed game mods, game design documents (for games not yet made), and (in conjunction with game development students) completed simple video games.
You may be able to see why game designers are rarely hired straight out of school. Experience counts for a lot, and of all people on a production team the designers are most able to completely foul up a game. In most cases, the designer begins as a tester or programmer in the industry, or as a level designer.
Because there are relatively few jobs for graduates as designers, many game schools devote little instruction time to game design, and not much to level design (which is a subset of game design). Unfortunately, "game design" sounds much cooler than "game production" or "game development". The big problem, then, for those wanting to attend game-related curricula is that schools often accidentally or deliberately mislabel what they do, most often labeling as "game design" a curriculum that is all about programming or art.
For example, I encountered a university recently that teaches 3D modeling, with a couple game-design-related classes. Yet they call it "game design" and claim that 3D modeling will lead to a game design job once you're in the industry. I cannot think of a single game designer who started as a 3D modeler (I'm sure there must be some). Designers tend to be people who started in QA and other ancillary parts of game production, not in art. (This particular school is in England; the problem is not confined to the United States.)
Similarly, there are schools that say they teach "game development", but in practice focus almost entirely on game studies or on programming. The latter is especially confusing. A "developer", in the computer world, is someone who creates software, whereas a "game developer" is someone who creates games whether by programming, art, design, sound, or other means. This is why "game creator" would be a better term, to avoid the confusion with programming.
So how do you as a prospective student tell what's really happening? First, find descriptions of the required classes. Often this will be enough. If most of the required classes involve programming, it doesn't matter whether the school calls it "game design", it's about programming. If most of the required classes are art/3D courses, it's not game design, it's game art. If most of the classes involve studying and analyzing games rather than designing, programming, and doing art for games, then it's game studies, not game development.
If the descriptions aren't enough -- and sometimes descriptions don't match reality -- then you'll have to try to talk to a current student. Talking with the instructors may help, too, but this depends on how much the instructors are responsible for the mislabeling of the curriculum!
Finally, find out what the background of the instructors is. Have they made games? Look at their resumes and their Web portfolios (they have one, no?). (Few "game studies" people have actual experience of making commercial games.) If teaching game design, have they had games published commercially?
Few schools actually teach game design on its own, without a lot of associated game production classes. In my part of the country, the only one I know of is Savannah College of Art and Design.