Terminals are storage facilities for cars (aka towing/flatbed services).  When opting for such services, you are responsible for getting the car to a terminal, from where it will be picked-up by the carrier.  The carrier will transport it to another terminal close to your destination location from where you will be able to pick it up.

When are terminal to terminal services preferable?

You, or another person designated by you, must be present for releasing or receiving your car.  There may be a situation in which you are unable to do that. If you want your car picked up or delivered on a specific day and you cannot allow a window of at least 3 days, there is a chance that your shipping agent cannot find an available carrier.  In this case, it makes sense to drop your car at a terminal where it can patiently wait for the carrier.

This does not necessarily mean that your requirement for a specific pick-up date implies you will have to work with a terminal. Talk to your shipping agent.  Carriers may be available or arrangements can be made – but the price may increase, since both the shipping agent and the main carrier will have to design a new strategy to accommodate your request.

Are terminal to terminal services cheaper than door to door services?

Depending on the amount of time that your car will spend at the terminal, you can end up paying more than door to door services. Besides their one-time fee, terminals may charge daily storage fees. If these accumulate, using a terminal will lose its initial advantage of being the cheaper alternative.