If it's entire within one state and not part of the original national system, it's normally done by Amtrak only if state-supported. See: Surfliner, San Joaquin, Cap Corridor, Illinois services, Empire Service (if they finally convinced NY to kick in a dime), Valley Flyer, etc.

If it's within a transit agency's boundaries, local service is a transit line. Metrolink covers a large area, considering the size of California counties (San Bernardino county is bigger than Connecticut). The transit agency can, of course, contract train operation to anybody including Amtrak, and Metrolink has done so in the past; the other operators are less expensive these days.