The phrase “Dungeon Master” is a registered trademark[1] by the rights holders of Dungeons and Dragons. DM is the abbreviation of that, and most likely safe to use.
Game Master (GM) is used as a generic (and game agnostic) term.
Edit:
I have (twice) edited this now after additional information from others (thank you Kichae for the link to the Dungeon Master trademark) was posted on this thread.
I don’t think DM is a trademark, but if you have other information feel free to provide it. Looking through older discussion forums on this topic, the only semi-definitive answer I’ve found is in this 2021 thread where somebody referred to a now-defunct US gov’t trademark search link, where they said they found a lot of "DM"s registered but none related to D&D. I’m inclined to believe it was a working link at that time and they weren’t just making shit up.
Personally I use the term DM because I’ve mostly played D&D, so to me it’s more natural.
My primary source at the time of posting was a sentence in the Wikipedia[1] but I have added the link to the trademark[2] that was provided by Kichae and rephrased my text now.
Thank you for reminding me that I should always properly check my sources and provide all information.
The phrase “Dungeon Master” is a registered trademark[1] by the rights holders of Dungeons and Dragons. DM is the abbreviation of that, and most likely safe to use. Game Master (GM) is used as a generic (and game agnostic) term.
[1] https://trademarks.justia.com/742/64/dungeon-74264094.html
Edit: I have (twice) edited this now after additional information from others (thank you Kichae for the link to the Dungeon Master trademark) was posted on this thread.
Some other games use other terms. Like wod uses “storyteller”.
GM is the generic term
I don’t think DM is a trademark, but if you have other information feel free to provide it. Looking through older discussion forums on this topic, the only semi-definitive answer I’ve found is in this 2021 thread where somebody referred to a now-defunct US gov’t trademark search link, where they said they found a lot of "DM"s registered but none related to D&D. I’m inclined to believe it was a working link at that time and they weren’t just making shit up.
Personally I use the term DM because I’ve mostly played D&D, so to me it’s more natural.
“DM” is not a trademarked term, because it’s a pair of letters. “Dungeon Master” is absolutely a trademarked term, though, and has been since the TSR days.
Thank you for this information, I have added it to my original comment.
My primary source at the time of posting was a sentence in the Wikipedia[1] but I have added the link to the trademark[2] that was provided by Kichae and rephrased my text now.
Thank you for reminding me that I should always properly check my sources and provide all information.
[1] https://en.wikipedia.org/w/index.php?title=Dungeon_Master&oldid=1185015796 [2] https://trademarks.justia.com/742/64/dungeon-74264094.html