IIRC Class c is boilers only, b is boiler and equipment, and a is both b and c plus a turbine.
You can get a special license by taking the test and passing, 2nd class requires 1 year of operating experince, 3 years for a 1st class and 5 years for a chief boiler’s license.
IIRC Special is low pressure and under 30 hp, 2nd is 100hp, and 1st is 300 hp, chief is unlimited.
Classes are more of a what you need and experience type of thing, I do believe you can be a chief c/b operator (b for sure)
Test and such are under $75 I believe, I think a special is cheaper.
Chief A license holder since 04.