I think a more pertinent question might be (in some cases), "what determines what a commuter or intercity train is?" The Capital Corridor is technically considered an intercity, not a commuter, route. I've heard it said that it depends on the funding, and the entities that provide it.
Regarding checked baggage on the San Joaquins, there are California Car coaches (8200-series) that have a large portion of the lower level taken up by a baggage compartment--look for the blacked-out windows in the doors at one end. If one of these cars is not availible, they "do the best they can with what they have."