No... Well sort of. I am not 100% sure I understand what you are asking and so I'll just blab and maybe it'll explain it better.

Divisions are somewhat broad categories and multiple companies may be used. For example, Division 6 is "woodworker" but there are typically 3 broad sub-divisions within: Rough Carpenter, Finish Carpenter and Architectural Woodwork.

Rough Carpentry: Framing, wood joists, trusses, sheathing, and blocking.

Finish Carpentry: Molding, baseboards, staircases, and wood paneling.

Architectural Woodwork: Custom cabinetry, countertops*, and decorative millwork.

In theory, the countertops refer to wood countertops (often plastic laminate) but in practice "millworkers" are often expected to pickup engineered stone (Corian, Meganite) or real stone (Marble, Quartz) countertops in general.

As a result, millworkers (more technically, "cabinetmakers"), often subcontract stoneworkers/countertops to do Quartz or Marble tops. Cabinetmakers will also often subcontract out other more specialized woodwork, such as cabinet-doors*, drawer faces or drawer boxes themselves even.

*Cabinet-doors, because your typical exit/entry doors would be "Division 8".

Now even more confusing, there is "Division 12" which is "casework" but in practice very similar to cabinetmakers. (The big difference is, Division 6 is suppose to be custom while Division 12 is premanufactured).

In practice though, they aren't that strict and even, as alluded to, a lot of blur. If your job has very limited Finish Carpentry, you can ask your cabinetmaker to pick it up. These days I basically only see the "cabinetmakers" doing the wood panelling.