I think its Shakespeare who has the famous quote "What is in a name? Would a rose by any other name not smell as sweet?". Honestly, I've never much liked this quote. Names are powerful things. They not only give you power over the item, but they also have a lot of power over you - even if only temporarily. Think about it for a second. If a rose was called a "Smelly fart weed" we probably wouldn't like them as much as we do. We'd be a lot less likely to stop and smell them, that's for sure. Now, yes, maybe someone would - someone always will - and they would find out that the rose actually smells nice, but a lot of people wouldn't believe this person, and still others would forever have their perceptions impacted by that name. In the RPG industry you don't need to look much further than what the person running the game is called to see this. Don't believe me? Well, let's keep going.
The Many Names Behind The Screen
When RPGs were getting their first start, back in the days of Gygax and transitioning from table top strategy games to something closer to what we have now, the person in charge of the game was called the DM. Now, DM - to the best of my knowledge and exposure - has had two meanings. The first is 'Dungeon Master'. It is a clear definition of what the person is. They are the person in charge of the dungeon and the monsters and things within it. The players move their characters through the dungeon made by the DM, and fight the monsters and obstacles that the DM has put there.
Eventually though, RPGs started moving away from the dungeon crawl with a story attached, and started to become a story with some dungeon crawling attached. At this point, at least in some circles, the D in Dungeon Master started to stand for something different: dragon, as in Dragon Master. It is fitting when you think of it. Dragons in those old fantasy games were often amongst the most powerful of creatures, the things that campaigns would conclude when the party had defeated one. The person running the show, was the Master of these magnificent and powerful beasts. With both versions of DM, you'll notice there is some level of inherent belief in DM vs. Player mentality. This wasn't necessarily the case, but it was inherent in the name.
Next, at least in the main line of things, RPGs started to move out of High Fantasy. Modern day games howed up, sci fi games showed up, super hero games showed up, GURPS showed up. With all of these, it made no sense to call the person running the game a DM because there were neither dungeons nor dragons in the world. Instead, the title passed over to Game Master. The master of the game, or, in other words, the person in charge. It was fitting and apt, and has seemingly taken over as the default term for a person running the game. There is still potentially some lingering levels of the 'GM vs PC' view inherent in the title, but this is heavily mitigated by the fact that 'game' isn't something that shows up in my campaigns as something for PCs to beat.
Finally, in the main stream games at least, White Wolf decided to go a different way when bringing the World of Darkness games out in the 90s. They didn't want to focus on the 'game' aspect of RPG, but rather on the stories being told. In a lot of ways this is the first serious and successful attempt for RPGs to try and break from being games and be taken serious as a story telling medium. With such a goal in mind, White Wolf named their GM the 'Story Teller' and charged them as being the person in charge of the tale being told. The PCs controlled the main characters, yes, but the story itself was in the STs hands.
Aside from this, there have been a number of other terms that have popped up for GMs over the years. Some games call the GM the 'Game Referee' or just 'Referee' for short, charged with making sure the rules of the game are followed. Toon called their GM the Animator, giving them the role of the person actually making the cartoon while keeping the feel of the zany actics going on. Other games have called the GM any number of things including "Game Organizer", "Admin", "Control", "God" and almost any other term you could think of for the role.
So, whats in the name?
For most people the name is just the name. However, the name themselves has an impact on the feel for these games. I already mentioned above how Dungeon Master and Dragon Master can give a feel that the DM is opposed to the players. After all, Dungeons and Dragons are obstacles put in the players way that needs to be overcome, and the DM is the one in charge of those things. The fact that old games did have some of this view present, leading to the current stock character of the 'evil gm' is evidence enough of that.
But lets look at some of the other terms:
First, lets look at Game Master versus Game Referee or Game Organizer. These titles have very different meanings. In the first one (GM) the GM is very clearly the person in charge of the game. The title brings with it a feeling that they are able to call the shots for what is going on and what happens in the game. The other two, Game Referee and Game Organizer, remove a lot of this power from the title. A referee isn't someone who can change the rules, they are someone there to settle disputes and make sure the rules are followed. An organizer is just the person who sets everything up. Neither of these give a sense that the GM can make or change things as they see fit. Not necessarily a bad thing, but it is significant.
Now let's look at Story Teller and Animator. These titles take the focus off the rules of the game and focus on what they want their game to be about. A Story Teller tells stories. An animator draws cartoons. That is what WoD and Toon are about (respectively) and this title gets it across quickly. They also show where the emphasis should be - the experience not the rules - in a quick and neat little package. Finally, they both also give ultimate power to the person running the game in a real sense. The animator is able to do as they see fit in a game. A story teller can change whatever they want in the story they are telling.
Which is right?
Honestly, that depends on the game you are running. The point of this article isn't to discredit any particular title, but merely intended to point out that names have power. If you are changing a name just to make your game stand out a bit, you need to be careful that the name you choose is conducive to what you are trying to do with your game.
Personally, I prefer GM. It is simple, well known, and gives the power over the mechanics where it is supposed to be. The power over the story, in my opinion, should be a group effort, and narratively the GM is as obligated to the players as they are to him/her. The rules on the other hand, should be up to the GM to make calls with as they need to. If they want to play fast and loose, they should be able to. If they want to go by the book, they should be able to do that as well. Obviously, I prefer whichever is done to be consistently done.
So, put some thought into it, and make the right choice for your game.