There are different terms for people who run Fantasy TTRPGs - IMHO this is how to quickly refer to those different type of Fantasy TTRPG Game Leads -
Dungeon Master - Someone who runs Dungeons and Dragons 5E as their Primary Game (at a rate of 51% or more of their Games) \ Specifically someone who cares about the Present and the Future of Dungeons and Dragons
Dungeon Paster - Someone who runs Dungeons and Dragons 1E, 2E, 3E or 4E or BECMI or BX or Moldvay or Holmes as their Primary Game (at a rate of 51% or more of their Games) \ Specifically someone who care more about the Past of Dungeons and Dragons than its Future
Relic Runner - Someone who runs TTRPGs that are copies of Dungeons and Dragons 1E, 2E or BECMI or BX or Moldvay or Holmes as their Primary Game (at a rate of 51% or more of their Games) \ Specifically someone who wants to play Dungeons and Dragons without playing Dungeons and Dragons
Additional Terms -
Dungeon Faster - Someone who is brought into Dungeons and Dragons 5E as a player with the specific intent to move them into a Dungeon Master position within 1 month of their first game \ Specifically, this done to make their transition to Dungeon Master move “faster” than is normally achieved with the intent of molding a skilled player and skilled Dungeon Master (in a single person) in as little time as possible