For the purposes of larp.me
A faction is a system-level division of characters. So in some places it'll be Nations, in others it might be Collages, Armies or even actually Factions. Characters can be members of Factions directly, or indirectly by being a member of a Group. So, for example, the system designers may have created the Grand Nation Of Mocktart as a system faction.
A Group is a collection of characters, usually under a system Faction. So the Grand Nation Of Mocktart might be a system faction, but within it is the Honorary Order Of Cantaloupe, to which a selection of Characters (The group founder Ameth, played by Amy, Brilique, played by Bridget; and Callum's character Callas).
Collections of Players (as opposed to Characters) are referred to as Cabals, because making "group" mean different things on the same website makes my head hurt. So, while Ameth, Brillique and Callas are part of the group "Honorary Order Of Cantaloupe"; Amy, Bridget and Callum might be members of "Castle University Plunder Pitfall".