A box truck that quits on a Doral side street is a bigger problem than a car doing the same thing, and not only because it is heavier. It is usually loaded, it is usually blocking something, and the wrong tow truck arriving is not an inconvenience - it is a second wait while a bigger unit is dispatched.
Doral is where this comes up constantly. The city sits about one mile from Miami International Airport and twelve miles from Downtown Miami, and the warehouse and distribution corridors filling the map between them run delivery vans, straight trucks and tractor-trailers all day. Here is how to tell, before you call, whether your box truck breakdown is a light-duty job or a heavy‒duty towing job.
The short version:
Gross vehicle weight rating, not how big the truck looks, decides what class of wrecker is needed.
A loaded truck usually cannot be moved as-is; the freight has to be accounted for first.
Federal rules require the driver to be satisfied the vehicle is in safe operating condition before driving, and to report defects at the end of the day.
Where the truck stopped matters as much as what is wrong with it - a loading dock, a gated yard and a live traffic lane are three different recoveries.
The destination decides the equipment as much as the pickup point does.

Weight class decides the truck, not appearance

The single question that routes your call is gross vehicle weight rating, not the shape of the vehicle. A sprinter van and a twenty-six-foot straight truck look like different animals and can sit either side of the same line. Light-duty wreckers handle cars and small vans, medium-duty covers the middle of the range, and heavy-duty integrated units and rotators handle tractors, loaded straight trucks and anything that has to be lifted rather than dragged.
Florida sets the outer edge of what is legally on the road, which is a useful reference point for scale. Under Florida Statute 316.535, no single axle may impose more than 20,000 pounds on the highway, and the overall gross weight of a vehicle or combination on the Interstate system may not exceed 80,000 pounds including enforcement tolerances. Anything operating near that range is not a light-duty job under any circumstances.
The practical shortcut: read the GVWR off the door jamb sticker before you call, and give the dispatcher that number. It settles the equipment question in one sentence.

A loaded truck is a different recovery from an empty one

Freight changes everything about how a disabled truck is moved. Weight distribution, the height of the centre of gravity and whether the load is secured all decide whether a truck can be lifted at all, and whether it has to be offloaded first. A half-empty trailer with shifted pallets behaves nothing like a full one.
This is why a dispatcher asks what is in the truck. Refrigerated freight is a clock. Hazardous materials are a separate procedure. A load that has shifted after a hard stop may need restraining before anything moves, because the act of lifting redistributes it. None of that is visible in a photograph of the truck.
If the load has to go on somewhere while the vehicle goes to a shop, say so on the first call. Arranging a second vehicle for the freight is a different conversation from arranging a wrecker, and it is faster to start both at once.