"Light truck" is slightly more formal way of saying "pickup truck." And is meant to differentiate the class from commercial trucks like moving vans, dump trucks, and semis.
Smaller pickups like the Ford Ranger and Chevy S-10 are in the "compact pickup" class. (And unfortunately these are not sold in the US anymore. For those with genuine need, we either have to resurrect some old heap headed for the scrapyard or import them on the gray market from Asian countries.)
The Maverick fills that space but has limitations (less towing capacity than a 90's Ranger). I've seen it used by a ton of service folks that need a pickup but not for towing (1500 payload).
The Tread Unibody is describing a piece of equipment mounted to a regular truck chassis. Their product advertisement show they're mounted to conventional Westernstar, Mack...
I've always found that to be a silly distinction, like it's a thing that matters to use cases in the same way that axle type matters, but it's not the sole distinguishing marker of whether something is a "truck". There are various non-trucks that are body-on-frame - BMW i3, Ford Crown Vic, Suzuki Jimny, etc. (The highest-spec Jimny tows less than the lowest-spec Honda Ridgeline.)
I'm a little surprised it isn't a regular cab with the 2.7L V6 that gets the highest payload. But they manipulate the suspension components a fair bit between different models so it's not just going to come down to the weight of the engine. The Lightning weighs as much as a gasser F250 but still has a payload in the 1650 pound range; my guess (without doing any research to prove it, mind you) is that the Lightning has the highest GVWR of any F150. I think even the HDPP only gets an ICE F150 up to 7850 GVWR.
On a related note, we have some real candidates on the Lightning forums for being the modern "Danger Ranger" trucks -- turns out you can load a Lightning with well north of 2000 pounds and it still isn't squatting anywhere near the bump stops. Stiff suspension.
Nah, for me it's about utility. Big trucks are tools, and they spend much more of their lifetime putting that engine to use where nothing else will do.
The shocking thing about light trucks with fuel economy in the teens is that most of the time they never haul anything. They're driven to the grocery store and to soccer practice where they have little value.