So you have the Jedi and the Sith and those monks that guard the Kyber crystals, but what other organized groups of people are proficient in the Force?
There used to be a lot more, but they're now mostly Legends. In Canon, we only have a few:
The Jedi (duh)
The Sith (ditto)
The Nightsisters of Dathomir. They were a group of all-female dark side users, who used spells, potions, and incantations to work with the Force. Asajj Ventress was a Nightsister in her youth, and Maul was the son of one of their leaders.
The Bendu (perhaps). Star Wars: Rebels introduced us to a character named Bendu, an ancient and enormous force-wielder who rejected the dichotomy of the Light Side and the Dark Side, and instead sought balance. Bendu always introduced himself as the Bendu, making it unclear whether this was a name or a title. In Legends, there was an order of monks called the Dai Bendu, who had similar beliefs.
The Dagoyan Masters were very powerful Force users from the planet Bardotta who, like the Bendu, eschewed Light and Dark and sought to serve the whole of the Force. The Bardottan species were strong with the Force, but did not send younglings to the Jedi, instead keeping them to be trained as Dagoyan Masters. Early in their history the Jedi attempted to take Bardottan younglings, but...it did not end well.
The Force Priestesses were an unknown species or group or...something of mysterious Force-using entities who held the knowledge of how to preserve the consciousness after death. Whether they were physical entities at all is unclear. They lived on an unknown world called the Force Planet, or the Wellspring of Life, apparently the original homeworld of the midichlorians. They trained Qui-Gon Jinn and Yoda to preserve their consciousness after death as Force Ghosts, training that Yoda and Jinn passed on to Obi-Wan and, eventually, Anakin.
Whether the Force Priestesses were connected to the Whills is currently unknown.
The Church of the Force. We know little about these people, other than that Lor Sen Tekka was a member, and they had sacred villages. It has been said in supplemental material and comments by filmmakers that the Church of the Force consists of people who cannot use the Force, but still honour it.
The Guardians of the Whills, the monks who guarded the kyber crystals on Jedha, are not known to have been Force users. From what we know of them from Rogue One, they believed in the Force, they trusted and worshipped the Force, but they did not use the Force the way Jedi did.
The Knights of Ren are generally assumed to have been Force users who grew out of the chaos after the fall of the Sith in Return of the Jedi, but since the only one of their members we have seen is Kylo Ren we can't be certain that they were all Force users.
Other organisations are known to have existed that sought to follow or understand the Force in their own ways. The novelisation Rogue One gives us the following:
What is the Force of Others? to ask this, you must ask one question and a thousand.
To a cultist of the Huiyui-Tni, you must ask "what is the exhalation of the true, amphibious god?" To a Jedi, you must ask "What is it that binds and defines all life?" To a child of the Esoteric Pulsar, you must ask "Show me the secret pages of the Book of Stars".
To my knowledge, these are the groups that have been mentioned; there may well be others. It's clear that the New Canon is trying to expand our understanding of the Force into more than just Jedi and Sith, and to give us different perspectives on it.