Part of CSX - the conglomerate - is CSX Intermodal Terminals Inc. To my knowledge, all the CSX Intermodal Terminals are owned by CSX Intermodal Terminals Inc. While some or all of the functions of the terminals may be contracted out, those functions and terminals staffed by employees are all employees of CSX Intermodal Terminals Inc.
I'm not privy to the legal details, but CSX Intermodal Terminals Inc also has owner-operator truck drivers that are contracted (leased) to CSX Intermodal Terminals Inc. The placards on the sides of their trucks attest to this. They are highly selective about the truckers they contract with in that they must have 'very clean' driving history. The terminals are open to outside trucking companies as well, that have passed whatever legal, financial and security requirements needed for access.
Now comes the fun...each of the trucking companies bid on a regular basis to the freight forwarders/brokers for contracts to haul x number of containers/trailers per day/week/month to or from each of the terminals, be it CSX Trucking or any other railroad intermodal carrier. It's the freight forwarder/broker company that determines which railroad(s) and which trucking companies are going to be used at each end to get the containers and trailers from the shipper to the consignee. The main criteria of selection is most likely having lowest price. But the forwarders also need assurance their shipments will be delivered to the railroad safely as well as delivered to the consignee safely and in a timely manner. So trucking company bidders are, themselves scrutinized before their selection, and likely have some kind of contracts between them and the forwarders/brokers as well.
Add to this, CSX Intermodal Terminals themselves have a marketing arm that will solicit various shippers and/or forwarders directly for business. Obviously, for those shipments, as much as possible will be done by CSX Intermodal Terminals and their truckers, in CSXU containers, and CSX Transportation, of course.
Then throw in Schneider National Trucking and JB Hunt Trucking. Don't forget UPS, Alliance, Prime and many others, either. They offer the 'complete' solution where their drivers, and their equipment - trucks, containers and trailers - are all handled by a single company (except the railroad part). Because of their volumes, they put out for bid to CSXI as well as NS, BNSF, UP, CN, and other railroads' intermodal companies their needs...xxx boxes per day, xxx days per week, whatever. They, too, will take the lowest bidder for the rail-carrying-side of things. Once the railroad bid is accepted, and as every cost is then known to them, probably within 10 cents, the sales price of carrying shippers' products from A to B is then determined and presented to the shipper. The duration of the contracts with the railroads, forwarders, trucking companies, and everywhere else all have specific beginning and end dates. When the end date draws near, the bidding process starts over.
And for everything else that isn't hauled by a national carrier, the forwarder will deal with individual trucking companies, mostly 'regional' carriers, get their prices, and various railroad prices, they must also contract with a container-provider company such as CSXI, UMAX, EMHU, Pacer, Swift, England and others and get a price for 'renting' their container from A to B for a number of days. Then they mix it all together and come up with a quote for shipper XYZ in California that needs to move aaa containers/trailers per week to the East Coast. Of course, the forwarder has negotiated various volume discounts as well with the intermodal 'arms' of each rail carrier. So if they can increase 'their' volume on the railroad, they get a bigger discount as well.
It's obvious that a single container shipment, probably not to be repeated on a daily or weekly schedule (very small shipper) won't get a price the likes of what some big-time shipper gets. But even for onsey-twosey type shipments, if the price via intermodal is noticeably lower than that of driving it all the way, then intermodal gets it. Business is business.