There were originally seven Dwarf kingdoms, founded by each of the seven Dwarf “Fathers.” The most common to show up in stories were “Durin’s Folk” (also called “Longbeards”) which consisted of guys like Thorin and Gimli. Durin’s Folk were the friendliest with Elves & Men, and were also the ones who founded kingdoms like Moria. Dwarves are largely very secretive and reclusive, so it’s mostly Durin’s Folk, given their relative openness, who appear in Tolkien’s stories.
There are others like the Broadbeams and the Firebeards, who hail from the Blue Mountains and have a large role in the First Age. The other Dwarf kingdoms are place further East, and I don’t believe they have significant appearances in any stories.
I think most of the Dwarves in The Hobbit are part of Durin’s Folk, but by the time of the 3rd Age that ethnic group expanded into several kingdoms, like the Grey Mountains, Iron Mountains, Blue Mountains, Iron Hills and Erebor.
I have a theory that Durin’s Folk are really just the Dwarf race that looks more like what humans would call “Dwarves,” while the others had different appearances.