This is a model of one and here’s another- a person would buy a new or used Model T car, take out the rumble seat and build a pickup bed. There’s a name for these “homemade” pickups but I’ve forgotten it and I can’t seem to google it.
(Anybody ever drive a Model T, incidentally? My sister used to have one that did deliveries for her drugstore and I drove it a few times- it’s a workout that makes you appreciate the hell out of automatic or even modern day manual-transmissions.)
I’d say the versions you have seem were the Chasis-Only versions, with wodden truck bodies added, possibly by carriage-makers, cabinetmakers, or boatbuilders.