I'll take a stab at answering your questions. Others will correct my mistakes, clarify my answers, and hopefully add more information.

Tim

I have several questions about heaters for my '49 1/2-ton. In 1949, were heaters optional equipment, or standard with every truck?
-> Optional equipment

I've seen dozens of heaters advertised on e-Bay, but the one in my truck looks nothing like them. My truck has a "B&B Deluxe", which is a SQUARE box mounted inside the firewall. The hoses go directly from the engine to the heater core, so it appears there is no way to control the flow of hot water. Furthermore, my heater unit has no fresh air connection to the outside. It simply re-heats air inside the cab. I've never seen this type of heater discussed or advertised. I don't know whether I have a piece of junk or something unique worth millions.
-> Your heater is not a Chevrolet heater. It might be a GMC heater but is most likely a non-GM product.

The most common types of AD heaters I see on e-Bay appear to be Deluxe and non-Deluxe??
-> Non-deluxe heater was called a Recirculating heater.
-> Deluxe heater was called a, Air-Flow heater

Who manufactured these units and what was the difference between them?
-> GM (Harrison for GM?)

Does the Deluxe mount to the outside cowl vent for fresh air supply?
-> Yes

Do all of these heaters come with some sort of control mechanism for regulating the flow of hot water from the radiator?
-> No, but there is an after-market valve sold my many vendors that mounts on the water pump.
-> The Air-Flow heater has a control-valve mounted on the firewall under the dash (protrudes on both sides of the firewall, with hose connectors on the engine side)

Thanks for the information. I'm trying to decide whether to restore my heater or dump it and buy a Deluxe.
-> It has become quite difficult to buy a Deluxe Air-Flow heater with all the seals, motor control-switch, defroster cable-control, control valve and control rod. Even the recirculating heater has become expensive. Just trying to prepare you for the quest. I have bought 2 Air-Flow heats and the purchases have worked out well (both were missing minor parts and the heater-motor switch is hard to find).

You might have seen this link in earlier posts about heaters: 1951 Chevrolet Accessories Manual (thank, Keith Hardy). It has both style of heaters listed.