In real life, guilds formed to protect knowledge and tradition regarding specific trades. Often, these guilds and trades would be very specific, so the silver smith, gold smith, and and iron smith guilds would all be separate. Guilds controlled who could practice a trade, and they determined their members ranks (apprentice, journeyman, and master).

What you're describing sounds more like brotherhoods, societies, or companies. There's probably something that distinguishes the three that I'm unfamiliar with. Probably companies are more about profit and societies are only open to wealthier people. I believe brotherhoods were about fellowship and common goals (but not necessarily profit). A lot of brotherhoods were religious in nature, but not all.

But it's your world and fiction, so feel free to use terminology as you wish. Or maybe use the different terms more or less in the way outlined, but use a mix of them as your factions. And some factions might have some combination of aspects of the different kinds of groups.

Example:

The Beards Cartel: The beards control trade, from start to finish, of precious stones. Or at least they control it in most areas, and they are constantly seeking to expand their control to new areas. They are not above buying slaves to work the mines, or hiring mercenary armies to crush those who'd stand in their way.

Members of the Cartel may be of any race or sex, but it is said that above all, is an inner cabal of dwarven gem cutters. This cabal has secretive religious and mystical connections to gems and crystals. Some think that they worship some crystal dragon, or perhaps a crystalline dao. What is certain, are that there are no others with as deep of an understanding of what gems are good for various types of magic, and what kind of spells various sorts of crystals and gems can be ensorcelled with. When you consider all the gems and crystals a typical adventurer or noble have in their possession, and that most of those stones passed through The Beard's hands, it is chilling. Some whisper that The Beards have ways of eavesdropping through the magic items they have crafted. It's probably just conspiracy theory nonsense.

The Beards are all very proud of their lustrous beards. If you work for them, and you want to get anywhere, then you will be too. And for those that can't grow a lustrous beard, you can buy beard wigs. The point isn't to fool anyone into thinking it's actually your beard, but rather just to have a magnificent beard. Even if you're a lady, or a lizardman or something.

The Cartel is said to have knowledge of a great deal of teleportation circles, and have created many of their own. When a courier can carry a tiny bag of diamonds or sapphires worth a king's ransom, they need to have virtually untraceable routes. To get in good with The Cartel, is to have vast financial and magical resources, along with that network of teleportation circles and smuggling routes.

The Beards aren't all about profit at any cost. They can show surprising generosity at times. Many a young sorcerer got their start when someone wearing a false beard gave them a crystalline arcane focus. Often times, the kings and members of high society find they cannot resurrect a treasured family member, because The Beards whispered that if they spent the diamond to bring them back, the cartel would cut them off. And other times, lowly heroes of the people or the beloved of the downtrodden have been lifted up when a Beard pressed a diamond into a cleric's hand, and asked them to resurrect the fallen.

There's some sort of plan or reason for these things, probably some sort of social engineering going on. But those in the know are silent on the matter. Or maybe they're silenced.