A guild is a group of people united under one banner, one name, and one cause. A guilded character wears the guild's name over their head in <angular brackets>, can use the guild's bank, and can wear a guild-specific tabard.
Guilds - Lists all guilds on the wiki. Main category for guilds.
A group may be an alliance of individual guilds, a player-run town, a family, or simply a guild that, for their own reasons, doesn't choose to use the official in-game guild system (perhaps they're a batch of roleplayers that prefer to remain in a raiding guild). There is no real classification that separates a "group" from a "guild", though all in-game guilds should be listed under the Guilds category.
See our Groups.